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~~~~~~~~~1 ~ ~ ~ ~ ~ ~ ~ I i:: u lE . lE lriE tuuE o 3oEIr iE ii~ :in11E lE :i El io Il IlE ri I, Eli: E I n I,: El a~ ii Elo ~iLi El [1i rEIi: El -1 .1:] El~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~E L~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i y Ja Ite I.- Fla Is i 1. L.i e : An I.vs / /R e ea r (:li S ec 4 i o n i UY u .a u i Ca stI a 1. D a t a A c: . u i s i I- oi on 1) i s i a n f B r.a (:: h (-.?s a nd Sh o r es. R.E F L.~ i di a 1) (..? p a r t men Y) Iof INa t1 ur a 1. R e To u r c e El LI~~~~~~~~~~~~31- I~A CHlE- AND11 *IAORr,'S El TEXHI..NTlCAl.. AND DE.SIGN ME'MOl-;1,NDUJM NO.. 1-34'K 3 El COASTAL ZONE E El INFORMATION CENTER El El R ev i e wec dlb y 1:1 Li ~~~~~~~Ec---h es and 9h or(:er, Rej1o ur c:e CetrEl :1:ns-- t ut e of Sc ien:ce~ and Pub In . i c A f f a i -'* E l1 o Lr i d a z-t -te 1.1n i v er 5 i A- y El l::l~~~~~~~~~~~~~~~~ and El El ~~~~~~~F I.cyr i d a O ff i a e o f C ,oanstIa I. M ana je me n t El 11:1 ~~~FlFor id a Dep a rtLment of E~nv ir onmone*a I. Re u [at ion El El Fundd cc iy 13 F. A grant- from the U. S. Of-fice of Coastal. Zone Management E Natiwi oa . Oceanic and Atrkiospher ic Adm in i strat io-n El El CundWer the (CoastalI Zone Managemeno-t- A)c: of -1972, ast amendjred) a I:: t hroaugh0 F lor ida Office of Coasta I Management i El P:: or ida Dep~ar tmo-n o'f Env ironmenta I Reg uLa ti on E F I.or idca Dep ar tment o f Nat ur a l Resour cessE GB ri~ 459 F56b uDEOJE~o~il~llJ~:III~E ~i]~~n~l:OI:EI:~olr~ El:3:IEEIIDIEIiIiOEr 1 I ILa11 0 1]::i a 0 :.Jia no. 84-3 Th e wiork p resent s a numeru fit .,T C a 1.c des C. r. p pt i co, n o f ". i t C or - 1. w a vc mecffe ha Y- i c Ai. d u e t o) sh li e-bT I r 'ea 1 T- ng f) nd u c (.?d b y th-1e preSeniCe of submerged I.oghresa-nd ba-r-s, a-nd -the e~Xpei~:: tedc c:h1ia r a c: t e. r i, I it (:., o f r ef o r i w a ve s. i e , ,h e i g Ih t , p er i o d anrd Le-in g-thIi fol[low i n ar- ra1<in sh ou I.cd wave -r eforfrma ticon be.. pocs .5. i: I.e .(.. . It provides -the basic: support mfethodo Iogy -f-eqIjjI red inv the de-:ve lopmenit of a mu l.t Ip Ie shore--breaki-ing wave tran~o mat nmde . diescr ibed ifn5 bsqun w o r Thne work1 descr ibed hereini constli-t utes part ia I fu I. fi I meint o--f c:onrvrac tualI. obLi gat oi os w ith -the F-edler a Coast aL Zoine Manrageme~nt Program ( Coasta l Zoine Mtna geme-nt f-c t of '1 972, as a mend e 1dc ) 1 r ouLg9h the F I.or i da Office of Coast alI Mayna gefi-en t sub i:ttopr o v i s i onrs cf c: o n t r a, c: t C MK37 e -n t i t 1. ec d E1n-ig iv nee r iv ng S up por t lE.rh la-fnc:emeni 17Pr og ram ' j [d pr ovisiru (:.s f N-IF! con t-ra c:t Ck)037 , Jt h i s wtcor k< wa s r (..v i ewec b..y t he !-.'earch-,es anrd Elio res FZFe..so)ur cC.. Ceinter , Irnst-i-t ut e orf Sc:i enic e anld Pulast~ iff s FI rI tt [in i v er s i ty The clc:~:ume-ivthas beeni adlopted as a B~eac~hes andj 91h-oreS Tcch-in ic:aLI and Des ig-1n Memor and cum ir W :cc' ia ce It h pr ovs onsof Chap-ter 1 6F-33j F'I.aor ida ~dmin ini st rat ive Code. (.'At the t imc.~ o f sub m ssi.Soin orc:on t r ac-tur a l c:ompLi a nc:e, James H. '.a I. s i [Li e was -the cointract1 maniager an vi d A lm i i i 5 trT a t C)r of the ~n i. ys is/Researc Sect i n, H a L Flea n as C h i e f o f then T'iur-c a u o:)f C oa st a 1.L Da ta P c q. u.i s i t io n , D)e b or ah E. F Lac:k Direct1or of the D;Pi v i si o of '(3ea c:h(.es a-nd Shores, anid Dr~ l:.lton J. G i. ss-ndia~nner thne Evecut i-ve D irector of -the F [or icda Dea etof Nat ur al. esocjurY c: es Del::'rah E . F Lack, Di)rec tor 1) i v i .5 i on oyf B ~e a C -i e s an-id 'Sho()reL1s Cy,\ ~~~~~~~~Janjuary, i9834 proprtYof csc (I.S DEPARTMENT OF COMMERCE NOAA COASTAL SERVICES CENTER 2234 SOUTH HOBSON AVENUE CHARLESTON, SC 29405-2413 INTRODLICTION 2 L~aboratory s'7tud ie~ IQ SOlLITM-1S AND koLN(*ID~JE AVE. DIS'FE-REI0N -1 F 'I'lE.I: I.ONG'SI*42RE SAND 'E{AR i 9 W4AVE- E1IE::G~lT ATTENUAIIITON 3. - WIJVE PER,:OI) ATTENUOIJA ON 3 kiA VE L.E-N G TI1- A T'rEIN UATT O N 4.", 41 P0.5,T-:AR' BIREIAKI<NG NXlSTANCE- M E SUIRE S' . 14 c~~~osu~~~~u~~~ ~~~ 47 RETE-RENCES ... 483 ATTENIJAT' ON OF kJAVE cIRCER:ir~FOLI.A..OWING hRE*RFA :c OiN LOiJCS!HORE SAilD BARS,! by ~Jamfes 1-1 . 13a Ls i I. i e Ania Ly:E i s/R esear ch Rec t i on , Bure a ut of Cc asta.- l. Da t-a Acqi.u is i 1- iocn, 1 ) i v i s i o n o fr L Bea ch e s a r dE -iT o r e+ s F L m-r i d a : e p a r t1 mien r, o f N a I- r a L Rer~soau r ces , 35 (O Co ommo n we a I. t i 'B L vd . Ta L L a hassE.e e ,F I 2 The geoffefiry of I. it I tora L pr of i Les may be s im(p Ly descr ibed by a t--- ri nsc e-n d ent; a L powDae r c: ur vye f un-ic t i o n ( Br vt t in i 9154 ; I)ean -1 977; I** u 9 h e s a nd C h i , -1 97 :E c) or b-1y appPa r en v y 1 I t m a t- e c com p Ie x i t y d at to oC. C : a r r en.-1c e o f ILC onI si Ior) e b ar .w vhI i c hn c: aof nnc)t b e s ;, fip ILy c! c i b)e d 14Wh i Le L oingshor- bars are producedl by weaves. (wa-ter ecve 1. r i g.e be i rig i opor t anti ) , they a I so ar i nstr umenrt a I. I- n 1- -f I. uen1C i nfI pOs t-irinc: i d enY t w a ve chna r a c tke r i s t i c s- Ava i 1. ab 1. e f i e I. c a ndc La bc)r a 1- orI- y d. at1 a a re u se d t-o d eve I. o p a m athI e ma -t i c: a . ci e sc: r i la- -t i on o f w aveo -tr an s- s onisi- )T f o I L.o w i ini I o. n q.sho C r e b ar i -n c i cl * n r e The d escr -I- p -t i on r a s su m es thIne de(:s I qnr c a se whne re -t-he L. ongvs h or e ba r b ed for m Ihas b een- pr--od uced or i s b e i in m ia i n-1t a i rned b y t1he i -ric i -- d eint wavNfes wh, i c: In b y d ef i -n i t i oin, mous A b e shor e--br ea k< i ng anrd in-c -th e p L. unI- g ring - -t:y pe c at- e 9 o r Y . 1a vye hne i g h t- r e f or mia t- i o n f o LI . o v i in stiore(2-br--ea k i ing over I. oing sh or e b a rs i s q i yenl b y Nb~~~~~~~~~~~ where I.-r i f: the Beveragje re-formed w;,ave hie i gjh-t , I-l i -thes El." e" b r ea k< 1 nig w av e Ihe i gi t ov er thIne b ar c: re s t , anrid T i E t Ine b a r n c i d en- t wa veP p er i o d The r ef or med wa ve p er i od Tr i is gi yen~T IbY T r ~ ~~~~ 131 V. (t ai~ In. Nb) T T~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~* L -o ng st~ho)r e .i a -s a re f o u rld a .s c7hr a c t r i . c- a I .y p er- ma m en: or sa s (on1 a L.f a I u r e s o c: a t ed i n I i t t o r a I z on es- o f I a k es - a nd oc (_ a n Th ey m ay oc-c:ur si -ing Ly or i n a ser ies a nd a re a ssoc i a ted w i t h s-andy beaches and nearshore aea A s i mn g le b ar c o ins i :!sts of a r idye of sand separated from the shore.l~ine by a trough,. Aseries of Longsh ore bars c:ons i ts of a ntimb er of a.7soca ed crests, and troughs. They a-re def ined (U. S.~ Army, 1977) to be oc)ca t1e d a t t h e b rea k er p os~'i ti on- anld , a t [e a st i n p a rt, ar e e r odled o ut o f t he boc)t t omf b y t he f a 1.I. i cig b re a k er , n and t h ey s eem to : e r e 1. a -t e d Ito t -he (- lie I h t c) f thie l. a r g er b: r eak e r tI , th u gh not nece(:~ssar i LY -the h i g hes t. E va ns (1 9 40 ) a nd S'h e pa rd (1i 9!50 -3 r ep o i- t h atA p j.u n i my sh ore - b rea kers a re es se ntI i a I fo-ir l o ny~-sho-Ir e b ar f orma t ion. Shepard (1950) anld i l ien ( i976) reot that I. o n g sho)r e b: a a s cn b e dle s troay ed b: y sp I 1. . i my . sh o r e br ea k ers , a Ithou.9h- i n anr ex tensivye f ie Id st udy Haznds, (i19-76) observed that- pr -cm:Ati c:aIL~y al.lI. irn::icdent waves d urin the sud were of -the sp1 . i iy vari e ty a-nd t ha t even under .s uc h c:o-nd it i omS aweL- deve loped syst-em of I[onyshore bars pernsistied. The genera t ion , phys iogra Ph y, and movemeni-t o f I n hr bars have bee-n stud ied l:)y geographers, geo Log ists arnd coa.tal.i- eny ineers, for over a century, resu I-i-i m i-n a Lisi- of pubIi- cat ions far -too to-ng i t refer to here . Most of the ex is-ii ng work is co'ncerned wimith the formiat ion and1 bi_-hav icor of bars re Ia- -tivye t.o weave and water l.c.eve I changes. i e., i-lie ef fec -i of wa.-ves on -i-le str uc t ure~ How~ever , i n -hiiIs work, atterltir i cnIs foc used onl the effec- t-iha-i t-he ntnruc tur e has o-n -i-he wvs wh ich by comparison has reevdless a -itent ion in the LI tera-- W i -t h Ith e x c e p -t i on o-f se -- i sm i i c s~e a wve s w km i~ ~-n e n er a . e d wvi ves- prrod u'.-- ItIne ,]Io1: Icr i t i '.::a I. fo r ces, -to wt I-, c h c oa st 1a L s ir u c -[ u re s n a u r E a I r mIa n madle, m ay b e s; u bj c: t, cli ( U. Ar my 1 9 77) . Wh en e e f-,e eve ,/ntsi- . sch as S . C Y fto Fs a nd h u rrT i c:F a ne S i mp F a c t th 11e c coa s- t t-h e d e str uct-i v e potentI i a I o f wqav es i 5s si9n i i c antI Ly i ncr ea se d b e a u se . p T .)ropa,3a t- i ng u pc:'n t he ru per-,.--e I. e va t ed watr s7U r -fac ( c s-lorm surge) a cc ompan ing ex-tremne eventls, -the waves ifripacl- c:: a s a Le i evat ionsno-t no-_r-ma Liy a-t ta i ned( anrid areas c -tthe c:(.oa s t no c.t i ni eq. u I L i b r i urni w i *t w av e -frc, ,-aes_.. 'F.-t i:Es. her .Ug:jete t hat na * ur a I. Li *t tor al. p ro-fi (.e, s-hape may bedesc r ibed. ir n erms, of -the c omp Le x ity of -the geometVry~ The ~-ifmp Icst geome-try may be desc~rilbed bry atras ndnaI p ower cur qe f unc:t ion ( LrIuLn, i 54 ; Dean, 1 977~ Hughes and Chiiu , i 9*7e Deani ( i977 ) dleftons t ra -ted- bot-th t heoret- i c.a 1. L y a nd p hyrs c a 11. y tha t -th e smootho 0 .--. co nc a ve upinwa rd , e~~ q. vti i b r i umj -ne ar shonc)r e prT-o f iie mja y be(. g i y en b y d a8 x2/3 ( vih er e d i s t1h e wa ter-c d epr th1- , x i s -ie d i s tain cec o f fsh o re, and a. i s; the(i s h ape c oe f f ic(-ient -f or a s ft soot h pr)rof i L e g i y en b y 2/3 ~4/3 24_ E (du c as 1.5 /\-b(2 4)f /- inr wh i ch pfi s t h e f L uid mriaSssc dens i Ity , g i s t h e ac ce .e r at ion of g r a v i -t y E du i stI h e unr i -f orm fn e r aT y d i s., i p at i onr f a ctcir , db s t-h e w-iat-e r d ep thI-- a -t w h i c h Nh or e--- breca k< i n-ig c c: Lr S a -ind H b is:, th e srh c)r c- b r ea < i n g wia ve h e i g hi t O f -t he p T- i nc i p a 1. vi e s ig rj sho)r e-- 3 b-rr a k< r t- yp es: . . ae.. , sp i I. i -I ng . p L fail q i t , andI(: s urg c ig nI wa vces i h on -I- .y typ P.F.? I-, ch C I-: Lian s a f -t II fvte Li -II fo)r m eneg U I 55 -I- pat y t i on c on-Ist Y. a.j I It , s thInesp I i I. L i ng sh o -- c- br- e a 1,er kence , where- alt r hoe -bi ed I k d b AI.b = 2 E3 NMc C o wan -I 1 9 4 M unI., , -1 9 4 B a L.-i 1.1.i e, i 9 3 a c':1 u a t ion ( 2 ? c I: c: oe s 20( E du a.S 1.5 (3) I.c an teP -I. of SII t P Por a I .) p. r of n Ic cj eoe rr - a Th e m o~st c om(-,p I. e x nat1-ura I. I. it1t o r a I. pr-o f i I e co me t r-y Is chIIar a c t1 er i z e d b y I. onqls hoar e b ar b ed -foa rmf pe ..?rturb a t I onsI prf i I g e o te tr i c s s-u chI a s ste p p rof e I.c a re i I nt er-m ed i a t e b et w e.e -In te e xt1r :-,flees) No tr ac t ab I e m a th ema -t i ca I. d cscr i Pt 1 on, h as b e en d e v Lo~1.jPed f or s uch I pro f i L es ,a [tho ugh F i g u re -1 i 1. L u str Ia -t e! t hat werebar crestl aind bar -trough d ep-th.: s are conls id ered , -tile p ower cuurve f unct i on aippea-rs -to procv ide dcc sf . c scr ip-t ioni. :r-f n erms oif wmave ac-t i vi-ty, barred niear shore pr 6 II.es d if fer s-igini f icant I. y f1rom smoo-th power curve p rof iLes s irnce -they are: I ,a sso C) a te d w i t IIp I.. unrig iYI n sh Ior: e ~rca 1<er s anld 2,~ c: h a r- ac: tk e r - i zed by wave re-forma t ioin Pin tearms of -they destruct ive potenit ial. of waves,* studies h a ve shown k"tT- t hI a t. rIot 1 on ri y d o ID rc a k iTI ng anTid b. r oI., eni wave-~s rcs u I.-t ini Large-r i mp act prsursthaIi an ess deformed waves; iln dec-eper wa-t er , bu-t d ffr in magin Itucedepn I ng on t heshr-bra1<r tyPe inrfC- eas in-g -frmcI l s u-Cir, I n to C) I i L ri nyc to pLunig I n;g M i IL1 ecr Fe -t a 1. .. 97 4a , 1i 97 4b ,M i 1I. Ier , 9 76) I I I �7.A" - 2/3 dbt = 0.128 Xbt V 5 -- �9\ 4~,,,' . Hands (1976) 9V~- 4- U =/= 4 9 crest 3 - ,,9 14- (>trough - A 9Ir 10 ^ 1st Bar z2- / ^' \A o * 2nd " I 91*'- o3 16 1\0 A A 3rd 2/ 3 1 -~ 1B~o \ 2J3 a 4th dbt= 0.124 xbt A b 5 - A Evans (194_ 4- A 23 / 2- 0 100 200 300 400 500 x (m) Figure 1. Illustration of power curve fits to longshore bar crests and troughs for multi-barred profiles (dbc is the water depth over the bar crest, dbt is the water depth over the bar trough). Numbers for the data of Hands (1976) refer to averages for each survey. Wa v (. r ef ora-to a cn I o -I - .I w i rln.) In i t i a L I - sc.Ir-br I--ea r n rj ma oc:cc ur under c rt a i -I 1. i t t ora L bia I h-yue tr i c: i tn i ons I. In anII e t enAV yi Lv(- a i o r aI - tor--y nIv I-,s t i g a t i c;- Ion 1;j wave(. beW--? I v i cor o n f xd L.i nIIe ar b ed s, N a kra ftur I- Sh r i as~-,h i , an--Id -a s a 1< i ( 1 96 6 a) rep r *t - ~ ~~ th at whIIe re IthIe 1bed sLop isv L e ss IthIan- about 0,0.2 to 0 .03 , wave r eformati on s~ho-rtjeardc of shore c-b rca <i ng; is Liklk y. l f i n f1.act -the; I.ope of the i. inear s~egment connect irni -the Lonjishore Liar crest and -the .shoreci.ine is used as a measure, -the cr iter ion a ::'p ea r sto be1) :- a pp rop1.r i ate (F igutre 2).. (IIg Cnide(:I( -I in ad ition a 51 i l i L.a r ineII(-. to(. the b arI t I-o u hi t o p r o v;ide ( f ur t h er u i d aniri , a I. 1 ml t i n, slo.)pe tan Y1CZ , mIa y b e e ftp i r i c a . L y pr~-o po sed cl i n .. 1 u~ is)accordi ng to: --0. 137 d bc * O0. O 27 e wave re-format io-n may occ ur O i 3'7 d bc * 0 .. 027 c no wave reformat i on ]-IeI d~ c is thre water diep thi o-ver -the barcrs .1In - pie (af *thIe d i f f ern e s i nI ie h av i o r o f w a ve at:: t iv i t for-- thIIe ex, trI .I,(,ems o.f pr-o f i I. e ty-,p e s , i t1 a pp e arYs t Ih a t t 1-1 e e f `e c t i:: a r red L.i t t or a L p ro f i L e s on , w a ve: -a ct i v i t y r e q.u i r e; q u an-It i f i c: a t i o II i 'f s uc: h a c:t i V i t-y i sto c b e r espons a I hi bLya c co unt-Ie d f or inr c: oas t- a L e n gi n eer i nI- a s-se s smIe nt s Fo a . i. ow i-I ng ex t e ns i yve r-e v i e w c:'f t he a va i l. a b i. e L.i I er a t u rce a s et cof m ath e f)a t i c: a 1. d (.sc r; cp t- i on a r e h e re i nIc dev e Lopr)e d t c:' d esF.c r- i b e w.)av-,e I r- a n smfti~.-i o n f o 1. ILow i n g s h orIe L., rcea k< i rnci o ve r L onc s hore I- ::' - a r" a .~ r a m e -t e.!r s nIIc: Laud e thIIe w a ve h-Ie i r~ I t , p er i o d an LI(11 e n t AhI 0.10 I I I I � Bar Crest n Florida 0.08 - o Bar Trough 43 N.W. Panhandle (Walton Co., 10/73-11/73) 45 Lower Gulf Coast (Collier Co., 3/73-4/73) 49 East Coast (Palm Beach Co., 11/74-1/75) o 42 Lake Michigan (Evans, 1940) 0.06 - OO gO � 80 Lake Michigan (Hands, 1976) a o 0 tan a_ 0o * oQo 0.04 - 0.137 d -' o o .tana,=O.027ea bc -- *0Co oo o I� E~"o oDaoo 8N 00 008 o 0.0 ~ 1� A~rr .ae'I I I I I I I o f l 0 1 2 3 4 5 6 7 8 d (m) Figure 2. Illustration of the likely slope on which wave reformation will occur following initial shore- breaking, using longshore bar crest and trough data as a guide (d is the water depth over the bar crest or trough, tan a is the slope of the line connecting the measured depth and the shoreline, and the plotted equation is evaluated in S. I. units). T h ee f fe c: t *thIna t1 l. nri:5sh or e.1 bars have co n a t t e nua t i ng_ C.v ac: 1 i v i t Y h as r e c:: e i v ec d:oni c! e ra bI.) 1.a a te en 4* i o n i -n *t Inhe p u b L Ise Li t er a 1: '.n e. It i s riot sup r is ing4 therefore, that foLI Low ir nature's L. ad , c~ons idcera ti on h a., a Iso b.-een foc used cm L~ess mob i .e submerged barriers that can, be cles ig-ned to reduce the destructivye potent i a of anti c ipa ted -nearshore wave ac. tiv ity. Pr ior to any clef init ive iriforma tion on the-. effect of sub: (jler gec barr ier- -t o reduce.. wave a ct ivit y , i t i s under s tand - ab I.e -that Pr ognos tMi c~at ions were made us i-ng ava i . ab Ie theory. Eary . theorr et ic a 1stud ies have been pub: Li shed by Je ffr eys (1 944):1for s ubmergecd rec:t any u Lar bar-r i rs 1 ean (1 945), Ur se Li (1 947) and John (1'948)D for sub:mer gedc p Lane vert ica L b.-arr iers; L~amb (1945) for a step-type p~rofi Ic; and Heis(119,50) for s ubmery ecI'p La-ne hor i zon ta I. barr iers (seJohnson, Fuchs, and Mor ison, 9'51 , for a more det ai Led cis s n In, -the I rImhowever , so mcth at mnore clef I n itivye i-n for - mat ion has become --.vai1LablIc ~ Never the 1ess * beca use of the di ff1 cuLty in coL~Lect-inrg fie~d data a.I he t ime o.f Longshore bair formationl, miost fi e Ld accounts- are de.-,cr ipt iye. Labora tory inves-t i~a t ions have been c~ondutc::ted mh i ch attempt1 to repi. i ca.t e the effect of naturaLILy barred nearshores. Other Laboratory - ~ ~~ st uc d s a re c o n ce r nie d w i t h, f i x ecd , i m mo c bi-.e s ubim er ge.d b a rr i e r aSades ign a I teria tivye to protec~t the coast.. The review of precvi ou w.ork 1<is5, there fore , cons ider ed sep: a r a-e Ly i n terms,.1 of f le I.4 i nves tig a-t i otsancd L~abor atory stIud ies~ F i e .id Zt u i ics, ~Y rn-i e 9 96 9) r epio rts i* wo se(~ts AoC f f i e Ld oib e r a t i o-ns ot w a ves p ass: i nrig o ver a b a rr ed .1)e ar rn shore c.n I--[(a p e C'o di Hlli h i . th11e walv esC i d ci not s:,h (or e b r ea k o i- n te b:3ar , thne y w e re a -f f ec : t ed b y thIne sh no a ILi int b -)a th y me try o f thIie bia r ( i ,.e. t h ey: pea k,--ipi at]s i f t o shno r e b reai k . a~nd thIne inumb er of wFuaves shoret-ardc o-f the bar P~tas doubie -tine inumber ji n( i den 4to- the- C,[ ,.ar Hereporcts thatil a fter the Piave c~rest rpasses -the bar crest, -the -first part o.)f the -folI.I.ow i-ng tro ugh i:.)ec omes diep r essed over -the shior ewa rdc f l.a nki o:)f thie b~a r r e!Su .t-I ng irn sec:oindia r yg rav ity wiave c~res t f:rflma t ilon Wlood (.1170, 4, 97-i ) cojnduct ca fIe .ci roon i tor-I.-g stud i es_ oin iLak1e MiIc h igain in w "'iic~h in ine wave gajge~s were pl~a c:ed acr-oss, *the .it -t o r a I. zo( n e For the, I ongshcore bar iinves-ti gat i on, fonur wave g agqes w e re L o:)c a t ecd o n the (. s to ss s L.o pe . o f thIne b ar ,an I.IC f i y e g ag9es~ be tw ee -n t h e b ar c.r e st ain d sh o re L iine,.2 C Ov er 4C)()0 c Ions e Cu- t I e w aves w er e toe al u r eci? Cl , ih 1. he I .- ci om i na n I b I. ei- y< I. -' e b e i nig i p I- 1.1 in q TI- -.I..) a'i Lr c s t wa s L.oc(-.a ted (0 o b be iaow thIne st i L. L w a t e r 1 eve L. ( E W L ), a-. ni d thI e b ar -tr ough I i 2 m be (-4. ow t h1Ine SW L E ~uhIa y da a n d R ob ert-1s ( 1 9*77 ) p re se n t a r e 1.a t1 i o nsh In pi b etwie e n re f or foiled anyid i inc i c--?ien t1 w av es Lir e a k i nig o v ei. r i Ing i In co ra L r e e fs - = .(.) .-.() 8e) Li~~ i Piuih re Hr is -.the r e-fm-med wiave hne igh t Hi i s *the iinc:i denlt wave In i ght near LIr eaki< -- ng . an cf- 1)i~ s- t lIne Pja t e r di e p -t h-- o ve(-r I lie Lar ri e r c:: r e st In Te y a I. s-o r ep ort h hat thIne avre r a ge w a ve p ero L.a incdi war cid o f 1- lie(- reef (.- - s smota Li1. e r b-iy a boiu t E.) 1- o 75% t- i, a n thine w a ve p er Ioi (-)d o ff shIo r e . o ~ f t he r e e s 9 ead y ain d Co(- L em (11a11I 9'3 0) in sp ec t edc vear -1 1 c:a L a er i a L p hoto"-1- q r ap hlY-f r (3Fro N or t h C.a r oi n a a n d nio r th .)e Y.1C a 1. i -fosr n i a w h ;F c h d e p i c: t s h o r I.) re ak i n q o v er n e ar s ho)r e ,-a n d b ars Th ey rep or j te r at 1 I o of t he -r ef for fte d w av e L engt9 h t o t he wiav e L en t h 'ne ar IDA.r- h r eak i i9~I ~ r /Lto ra n ge -f r om 0 ,1 2 t o 0.~5 w i th es t i r a t ed v a L. u C o f theI r.a t i o C)of thIne r e f o rmied Ato in d e nt w a ve h e i g lit Fir/H rangi n g *f ro in 2 5 t o 0~5. i e t t e (i 9 80) r e :o rd s ha t hy te t r i c: , w avNYe h e i ~h t a ndc p er i o d c: ond i t i onrs di u r i -n a -1 9 7 s torm wi nh i ch, st- r tic: k, t he 1< i e L. :i g h lt (:: o as 1 c-on At lie TAa 11it I c: *9'ta , Amui II. t 1 - 1:3 a r' red r crof i [C a nd w14a ve lie i g h t a -t tentri a t, i aon f o L LowP i n g b ar -hI)r ea 1 i ng a re r ep or-t efd C a rt:e r a -rd 1-i a L. s I. L i em ( 1 9 833) reCpor.)T. t o Y1w av e ener Cg Y a t t en-1 ~IIa t io oc)v e r rnica rshIno re s and ( b ar at Loac::a L i t, i es i n F [o ar i cl a a ndc N or t In e r n Tre L-- .a nd. ( The-: d a ta are repo:r ted as shci or-hr eak1<er h-eights * from whi ich i t is suggested ( assumli ng, wave ener.ngy to I--e d i'rect.I.y prop orlti onja t. o t Iie~. sua re -:'FtIire wave hlieghIit ) Fib r Lo".b - 0~~~., 05 -If. 0.18 Lo:3. + i~~ [ib r Ib i/ Wj.i-r LI.-IHbi s -the kinc:i dent shiior e-b:rca 1er hici gh t over thle bear J.br i s t he r ef o rmred lIne i g i t at1 sec.-ao n d a ry s h or e --br-ea k i nlg s t Ii cw i di Ii o . f t lie i -nc i di e nt :b rcea k er z a fone anrgd i~l s thle wave sP e e d a t i nc i d enrt b a r -hrTe a 14 i nfg t...a 1:3 o r a t or "' t u d i .?s Th e -fi r st L ah)o ra t ory Y Ht IIdclY k n ownj t c.- t he a ut h or IIas5 c: oin (J II c -te d by Y tl uc(: 1< Y a nd B o n na r di ( 1 9 37 ., i 9 33 ) -1o t. eSt t -i e a nt i cI P a t ed C on,-ftr T.ut t i on oif a su~IIbmte r ge d b rea kw a t e r a t 0 pcor to, P (.)r t u ga L .. Re suLti ts o f ti c ei r wito rk I, 0 e xp er I fiie n ta . v a 1. ties) a re d'c: use c:.- H4 1 Y1a L . (1i 93 9, a ~pp er;cli x II: T'rhe f i r- s : d .e t a i l.e d s 4' u dcl on t he- s ub J e c t ifa s c: ond c u c' 'ted b' Hla L . ( (9 390) f or t h r nee s ubme r e d'.i :a r r icer c: onrf i ju r a t Ion s (I: i u re 3 R e su I. t s focir 6 4 e \ip~e r i o ment a 1. r u ns a re repF. o r t ed p r ov -q d i he i qj h t , p er i oct anid . e n g t h o f t he u n d e fo r m ed i nc i d e nt w a ve s a n d t he h e i q h 4' and Leng th (if the r-efo.rmed waves'., He dlisc:Us ses thc~efic-i'fc-l that subme-r-ged barr i rS hiave on at te-nuati 1ng wave he ight4' and -reports the wave L~engjth to remra in conserved, M a S onr anrd K eu L e q an1. ( I 9 A,44) i n ve s I i a t ed 'th11e e f f-e ct cof a te p -'t p e p: r o f i t e o.)n w a vf* e4 r a ns ss ooi5Eic)n f or m i I. i - ta r L a nd. i c: r a f t o p er a tI io nsA Th ey f o unrd t h at > -1 0 , m u I t i p L.e' w a ve c rests , w i L L .f ov. m s h o r e:.,wa r dl o f the s t ep wh ne re IH- 0 a nd- :' ari--e t he*. ci e ep wia-t er- t wa ve he- I gj h -t an- id I e n 4' 1-- r es p e t i y e L y Th e ir dia Ita s h o tIha t s h or e'br 1-ea 1< i rny. need n ot -n ec e s sa r i y oc c u r f or mfiu 1. t i p L ez . wa ve c.r e st f or' mnat i on. Er u a t i onr ( 7) waa s *fu r 4' h er v er i f i eci b Y i- o r i k a w a a nd 14 1 e qje 1. ( -1 95 9 Th e -r- csu I t s o f M as on anYid K eu L e ga n p r i ma~.,r i 1.y d ea L wo i th wma ve L enrg t h a t t e nua it i o)n T he a u th cor h a-s' f itt1e d an -f i u a 4 i on tl-o teI- r T d at a (8 epr Y.i m en ta L r esu I. t S;) t o Y i Ic I. c r (tanh 4.J3 F~j' 1 - -a fi ( 'I 9 45) r epor t s r es-u t s focr t h ree i ic: i d ent wave I 'I SUBMERGED BARRIERS V Hall (1939), > g Morison (1949) -O Hall (1939) dah 7 Hall (1939), Keady & Coleman (1980) STEP PROFILES Mason & Keulegan (1944) Putnam (1945) _ LONGSHORE BARS McNair & Sorensen (1970), v Sutherland, Sharma & Shemdin (1976) , ,,,,,,, Figure 3. General types of fixed laboratory profile configurations considered in the present study. oIn d i t ion o 5a v e r a s t ep p r of i be. e Th e se cia t a a rc p ar t ic(: u Lbar b.y v a 1. u a b b e s i Inc e the c: on 'It i-I II 1.1 u s fi as u I r e ften '1 o f t h e t r a n s f o rm i Ing wa v e snc:'tl o n by r o v i d es IIund e f or m ed i nic: i cd en ,- t a nd r e f or-med w a ve chIna rac teP.r 1st5 i c s b u: tt a [.s o w a ve c Ihar-a c:l ter i s t i c s a t thIne s ho re - b re ak i ngI F po sition N or i s oIn i 91 949) c oIn d uic t ed a se(2~r ies Cv f c x p erT i mite n t s focjr r ecc tang-qu,1 bar suIIb me r ged 1)a rr i e.~r s ol.. n hor I z o nt a L a ncl s L op i n-g b e.d � He re.p o r ts t ha t w a ve. n: hi gh t t raIn s mi ssi oin is5 a f un)c t i onT o f b..1a rr i er Yhlne i g h 't a nd1 w i di thI , anrd i nj aic I denrt wma ve ,s-t e ep ne s s: The s-t u dy is p art cu bLa r b.y imftpo r ta n t s i n cej p h o togqr ap h s are p res en-It- (rcl whI- i (--]I c: bear by i deil eti f yt ine brv ea k.,er- t yp e wheren-,-s : br ea. k i n11g occ ur red o-ver tine barr ier sA Th e f iI- rst a t t emp t at- c o mp r ehe -ns i y e r ev i e w ci su5.II b m erg9e d b a rr i er s aIn d e f fe ct o n w a ve( h ei g ht t r aIns it i s s i on i s prI-ese-ntIe d by ~Johnson , Fuchs, and Nori son (1951 ), formaLb y present inci the wiork o f Morison 1 949 ) Wave hei1g h-t -tr ansmin sion is re-p or'ted to be diepcend enl ton thne strutc:t ur ee ightanid barr ier w idct h re la~- t i -v e t o i In c i deLn t wax'f e c c inc i I ti orj . cir -F.hFi a b. bow w a t e r t he y Hrb -I (~~~~~~~~~~~9) w her e hnbc i s thIne b arIr icer h e i gl 'nI anr d i s thIne wia t er id e pth m ea- sured a t -the se award -toe of thie str uc: tures-. Eq{ua tion (9) i s app L i cab be wh-er-e db / (g T.f 2) ()00.155 on a step p-rof i Le. Equ a - o) n (9 *a i b. s , I how ev er , w h ere hb y' -1 . 0 i . ce ., t he b)arr,, i er cr e st i s c o I nc i d e n t w i th 'th e vwa t - ier stIIr f ace) for wAIlic Hr Ii=0 a c on--1d i t i on known to be trint r tu. Uinfor tuna'tec y, Jih nso-n , tch an d M o r i S onI- d ci dn-1ot pr TI -[ a II~ - o t hI C i Y- d a 1 a i r, o t1 II e rt h- aIn CIi oi (.en si i onII1 [C.. " t e r fl. r 1)i ephuI Ai s ( i9`57-1) inIIv e t1i qat1e d wiia ve he(?i gh t and laerI lod a tt enI- ua II on fo 1. 1. owV i IyI ni In c-i denIc e onI- a f i ,, ed I)a r --ty pe feat1 ur T-o , i nc r. utd - nq-I s e ver a L. c a ses wh -IerI-e thIIe shora I e --b .- r a ker t yp e a -n b e d e t er-- fi i ned . Unf.1,or Y t ti nIa t e 1.y thIIe (IIa gIn i t u de o f hIn iS w ave O(:h. a r ac t er i t i c:s w~ver e in th 1Ie r an ge whIIerY-e sr.uI -fa ce t enIs i onI anId v i s, cC)us e.-,f fe t s furth C1.Ie r a c centI u a t ed at ft enIIuta t i onI o f t he r e fo r oe d lie(- i qh t anvid p er i C)d . In-I anI i IIvest. i a t io-I on I ,I on sho e ---I:-r ea k< ng on q iIf i x (e d i, . i Inear ca opes , N a k< a Iu r a ':]- S I r i ash[ i an )I(: La k i ( 1 96 6a ) focunIId t ha t wh[Ie re thIIe s lo pe -tan IIab w.jas le ss th]Ian-- aI- abou t 'O . 2 t o 0 , w a ve rI-e formI-- (Ia t i oIn c ou [ dc) ocur f o 1. l. ow i IIg iI n i t i a L shontr e- br-e a k i II Th e a uthInor IIa s f i t t ed eq. ua t i ons t o t1he ir dla ta t o y ie Ld t he foc L- 1. cow i n-)g r e [.atii II- Inh i p si X ~2 6 i Hoi wh .- e r e I s- tI he d i s t anIc:e to wia ve r e f o rmtat i oIn foC L 1. owt i II i n.- i t i a I s-hor e brea I i Ing T r (bn i( tohIe re ''Ti s thIIe invic i d entI wa ve p erI i o d , Tr is -the reformed viave pler i o )d a. ri dib i st h e w a t e r d e p t II a t shorC I-e.- brY e a 1 i nIg In d 0 Ir ~~~~d b ~an -I- III L.b L whIIe re L b i s th]Ie w a veo I eg t h a t shIIo r e--b r ea k i IIg E-q. ua t i on -Ii 5 -14 a n d C 1 2 ) arT-e f or a i nea r b)e d s,1 lope of t1a n CZba () , K.) I A N a k4 am ur a, Sh i r i ashI i anrd Ea sa i< I C 966b ') a Lso i n~ve.s t i g at e d w av e t r a -n smii s s i on. i: ov er x e d r e c t angi u 1. a r b ar r i e rs o n a Ii o r I -.- z )r ot a I.1 bed T he yY fouind t he t thIne r at i o ojf t he r efoc)r med c t o inri- cid enyt u n d v. for T ( med w a ve Ihe i g h-- t , H-1r /l~H i , d e.p endF ls aon -t-he ra t i (.)o of t h e b a rr i er w ic! t h to t he inric i d e ntI wa ve L e ngqthIn, LO /Li arnd to thne ra t io of water depth over the barr ier -rc to the jinc..- den- iit w a ve heri ghItd, d/ I- A IT he a ut h or Inasr f i t t-e d eq u at i o ns t o thIne ir d at1a t1,o y i . Id t he f o 1.1 low i ng H r ~2 t ari h @P3 dl /I-! - @~~1> e (13) I.- wih ere: --I .002[/L = 04312 e (14) @2 hIS +. 1i (5) a n r db t 1[C �n. an d 0. 45 Lr dbN ylavl~i 0.75: bt where d bt is- -the wmater depth just Landward of the barr ier crest. 1 5 'Oic kj (1i9 63) -f ou nd that where. wave.; break, on a submerged Ubreak water , the per-i ad o~f -the re-formed wave wasr thle sm as5 t he(. inIIc- i dentI p erY i a d, a L th ou g h o th er r e o-I formed cre s-ts of L. e s sr li 'I g h an at h I c)-fhig h-Ier IFr egq u e Ic ies were s c u p er2 I mp sC.) C. t he -f u n danentI a L- refcormfted w a ve. M c-Na I -r anrrd 'S'o r-e n soan (1i970O) I n ve s-i I ga t ed w a ve t ra n sf or Ia - t ioc)n o f r-eq g u tar w a ves i nc i d e nt toc a t yp i c a L f i xed b)a r g eom) Iet.ry , w h I clih t hey d e sc ri be a s c ha r actIer i s t i c at L y h a vi ng a ge(~n t 1.y s . C)p i nclq sit ass f L aink , rou)tn d ed C-cr .' 't anIId s~ t e ep L I:i . c .) s Loe. Re - s-- u Li ts ai f 3'S5 e X Per It men I s ari -e r e p or tI-ed w herI-e t he i nc. i d en t wa v es a rI- r e La i ye Iy undc e -foar (Ie d lip o n rI e farI m a t i an f a I. L o w i nci 1 bar in c. i detn c: e , the w a ves ar---e re pcr ted toc b e i re re i l. a r- , i n t r a d u c: i rig cam p L.i C at ionsnr thati- re q u i rec--d s p ec i a L c: on s i dc.r a t i ons t o d e ter-m in e the reformed wave he i gts~., It i s repor-t ed that , ini genera l the wave peri ad didc not change foLLowing bar-Urea kring , al.-though i i a LLr e -for m edc w ave s a s e c:7 and a r y e nerg y p ea k ac(- c ur red' t h a t 1&'ta s c: jn s i st ent ILy t wi ce Ithe f req?,Lu en c:y of thati a sE.o c I a t ed w i t h tih r' in c i d e nt wve -ivo T h ey c: cn c- L u cde Iih at IH-r /H1 1 ls: cl e e nd ent- - pr i moa r L y o n t he I n c i d entI wa~jve he (i~ ghI- t a ndc the wa I erc dep tIiC) over tI lie z. b arT c: re Sa wara -I-.i an--d I:wa ta (1i97-4) inrvest ig9a ted share Ur ea k< i nIg o)n aI s I e p p r- a -f i L e , I n c L ud ci ngq w ave lie i j h t a t I en ti a -t i n a n d v arI i o u s pac)st --s ha)r e U rea k i n g m i Let~stI o ne ti e-a s tir-e s !Eq. Lta i C I. ns -fi itecidt - to h ie r- d a ta b y -t-h-ie a uthor arI- 1~~~~~~~~~~~~~ 9 x 7.5 L -2 f i7 0 H0 X a = L -(2.2) '.&he ere t d i s' t li (e ci i t a -nc: e- f r ( om shIno reb r e a I.,I n g � o) t he pin t where ':e 1- (.7 I unc I T-jv r te (I I. . e - c: 'r 1. o f th1-- p 1. 'iri I n g s- h or e- break en-) tC)uc h es ciciown onlto the wmal t U er Traca front i 'rig -th e h r ea k I n c rc e s 1 s t.hefi d i s tance 'F r (-)r sh In cyYe --b1. rca k i nc t1o th e po)i n t wh e re t1he p 1. u ng qi n g v o r ex r ea c:h e t he b ed x x5 is thIne N p L as h cii st-1a n ce arid (Jxa s *the d i st anrce iwhInere a i rf - Iub i1)b L es d: is a1I. p P C a i- c (fro t h e4 w.4a t e r c- 01 u ilni S utII- he r- La nd, h a r fia , i ad Sh-lemftd i n I '1 97) m o d e L e d a Ityp i c a 1. 1: 1,. i cia f eas cost 1-ircj f i i e -to i n veI i ti te r unup c:'c c. u r r I whIle re wia -vest Ii rs t eno te ai cI ors shor a r. . I a v/ e hre i 1 -1 dt ucl uc t i on-. f o 1. Low I ng. rb ar i n c: i CA e--Ic- e i r.eporp *t (Zcld Ba.it teies and J a nir.ssc ( I'1 9'7 8) i L Uts -ti- ate t viE) eX a f"'Fp L res otf wia v es p as I n o ver a h a it -ty pe p r o f i L.e ,a nd(: 'the t esL-u L t a nt w av e h e i ch 't re(.,d u c t- i o n e cacldy anrid Co ID. eran C i -i 980K- )I novest I icj a t eci -thnEn e f fecrC:ic -t o a Tra p ez c) I ci a I1.I b Lriimer ged ha, i-- r ri er i COn- v. In (:. r i z on '. a 1. b cc)C) TI a ' I ten-- uaz- t i rcj t -i e wva ve he .. i g I.I t. Th e i r s- t uci y was oi L i fil t ecci 't C) vci v eS to14h i c: h barE '-Ib-I.r c-L k-, c. aSw p L u ngf i -rig sF;h onr c.. -- b rcfea 1, e r. s a nci d - u g g ei~t -1? [E q ua t on- (23) .S 'if fr C) n C. owve r , from(I a S i fil i I.a r- pr oh I.) .cm? f a c I gl e q Li at i on (9).. .0 whe (j~ C C), *thIe v a L. uc o f IH1r /H iI T'S r. eptsents a non-c a III e.L va I ue ., They a I~so rep~ort that a grea ter number of re- foc)r m ed wia ve crI-es t s a re p r o ct u c ecl a S thIIe Va J.ue of d i s cd e cr e a s ecdi and ag dc i-ncr eases the r(- efor med wa-ve appears- as'l twjocrs . For th Lat ter c: a ce, one c) f -the c:r*est, t s becomes h i h er th.anl th.e C)t h er anid C hanry eis Pos it ion on the f1u-nd la ent a . wave. formi as -the W i.\SP p r ocr e s ses. SOL.ITONS' 4ND S..t~I0Nl.'.GrIND1JCE:D WAVF.IJ:PRSO Uind er c er-t ai n c:ondi It icons a sh oatirig nc; ave c::anr dcc:orp o-se II n-- to a tra in of waves (i.4e., , ou.Lt ip I c~rePt productior;)0 without the wvave-- -f Ir~stFbc y. Ga lv i n ( 1970) sl't uciIclj wveo:?rdr ndir a '-in fornm ci ep -t hcof. we.-tern where the waves.. wetc.-re s.hoa Linc; k .. e ..4 1/H1 I .. I 5an yj4Cl/I.. (). A3 ) He f-c:'tind t ha t the.. wa v~. broke.- dow-n i nIt o sever al waves ca L. L ccl s~o Li tocn s ThIIe samfte -I.r! s.u i. t c: an a pp1)a renIItl.y h e p ro)d u c: ed o v er a s te p pro c)f i Ice Th e t r a i n c f w qa v es pr- -odu 'c.e d arIec ch IarI cc t er i z ed by) a Ih i yhIest! f ir s-t for -e ce st- fc. Li1 o wled L'.. y C r e st s c f cicec:rcas i ny hf-oi(- :I. I e i g h t , a nd i f s C) Ii ton c)-5C: an- pr o paq a t e a s uf f i c.- i enIIt d i sta nc.e th-IIe c: re sts~: c anY r e c c)mb1- i nc an-Id a 9a inI s epjDar-a te inIt o so L i tnc)IIs. OthIerI s t ud i e s on-- thIIe plie nI r ~e n o II CIam(I f i (.e I -Ci , I 930 )a ar e rep 01.:--- ed b y HIr c)vik a w .ia IInd kl i eyge I 9 59) B . a-nIjam i II an- Id Fei r 1 9 67) S' 't reei-F t u L q ess- a nIci Ih 1,JI t f o r d (1 9 63 Maci se and M e i I(1. 99 ) .-:-a h.)ustkY andI a I v in II97 ) an- i. -- a nd �'orj -cl--sen e ( 1 972) anIId Ha Imi a c k an-Id S e LW I ( 1 974 -e Byrne (I i969 ) noted seaC.)n-d a -y wave are t form at ionm- fo I. Low- I.Iq[ n q . on-g sor e I..) a r i n c: i d e n (: e i n t hie f i e L d , i n w h i c h br--eak i rig d i d no t f i r st- iccaur ,Socmfiie s t ud i es, h av e s u g,-jes t e d t h at the observa- i on exemp Li f I s s-oli.iton for ma tion. Ee-. u a t i o)n ( 7 ) , (:1ev e Lo-ped b Mason andi Keu iegan (19?44), is one measure that can be used (s~ee d isc uss ion of Ca rlrf ie LcU, 198()O) to d eterm ine when muL t ip ie cr est formation ran occur, and does -not -necesisar iLy represent con-- d it ions w,,he:re shore-break ing occurs., Hence * i t is app arent that three c lasses of cond it ions occur when wavers encounter a 1. o n gh o I-- b ar I s.h c;a L.i n g wa t er d e pth a re gre-q.?a t e:kncrug9h thIIat the waves are riot affect-ed, 2.1 water depths are in -the range where- the waves dco n:Yt shorc-?-b-reak1, but do di sper se, and water depths are .i mit i-ing and shore--break i-ng r-esuL~ts. - t is th lis L~atter case, -viewed as a design cond i tion in L.i ttora l Pr ocessEes, th at de fines the focus of attention in th is p aper. THIE I.XJAi'HORE SAiMD 'I is ap pa rent from t-1Ie p:reccedji nc sec tki on_ t ha-1t transfor - mat i on of wave chia rzacteris t i c:.s fo l Low ing s-ub:mr-er ged barr ier i nc ici ence 1 s d ependent on many fa-ctors. Prl-iinc ipa l fac:t or s are -the lwater depth over -the b:arr ier crest, Libcl barr ier he igli-v measured at the seaward toe of -the barr ier, hb barr i er crest Leng th , Lb barrnei-e stass :s L.pe, -ran c bs. water dept L iand- ward of the barr i er crsdb an-d i rc i dTent wave charac: ter i r- t- i Fl s L , T , w i t ih c om itb i n at i cons! t h er-Co f , s-uch 1-1 s, Hi h w av e st1eepness., IHow)ne v er , in -,I+h i s pa p er o n 1.y nat1 u ra L L ()n qs1h orI-e b a rs c moe oaP()5(I()f sa ni-d - s i z ced s ed i men tr a re c o ns i ci er e d , a nd c: 0 n d i t i o n s may bie 1 imp1 Li-f i edi Nat u ra 1 Lo n gsh or e s a nd ba:rs- ar--e pr od u ceci b y sh]IcjIr e --b rea k i n g -19 wavl jes5 of 'th1e p 1. u ng i n g ty pe, a nd w a ter d e pth LiI ita c: l ns- c: an IDe cd e n t i f i e d T he r a t i c) o f w a t er cl e.,p tih to sh-or(.c--b rec j< r h e i g h t db /id1b Jh as b ee n foaunrtd B L i 1. 1. i , 1 5 sa~ : t o Ibe a cc urTa te I.y db ~ ~~~ L28 (24) HbI iL i. u st rat1ed i n F i gur e 4. E'q ua t i on ( 24) d oes nont , i n a I. p robIDa- ID i Li I y r p r es,-,enr t 1 hie wat1e r cie p t hi ov-ye r h he I La r (. r e~st ape x 'a t h er fhi he a ve ra ge b re ak i n g pn o s i t i o)n u nd o ubI tab ID y I. i kF Fs so me d i sI- a nc: e sge aw a rd o f th:MIe cr es apye x oe r t he: s t ois siope. ( c. F i e I. cl m e as>uresm ein ts o f s~h oDr c-:: r e a ri q n wa Ve acat i v i i y fo(Ir :s i ng Ie wr;a ve t ra i ns a nd a ssoc) c a te(--d s ur f z on e wji d t hs we re cb IDta i n ecd by a~ i. s 11.1. Ic anrid Ca rt1er (19 8 0) a nd s ugge st (FigurYe 5) t hat th e .su rf o ne W i di ti ) Iw b I m ay IDe g i e n IDy H7. b VJ ID ~~~~~~~~~~~~~~~25) id d i t i onia L L y, IBa L si L L ie an-rd C rter (1 984) found -tha t for a Fhorpe-bDrea <i ng wave tra in -the average shr-reakrle igh-1 and -the standard deviation, 5 b' a ssoc iateci with the aver-age can be re l.a ted ac-cordinig to: I. I. us-t rat1ed i n F ig ir e 6 A s--um fti nig th at *2 s b r e pr-e s-e nts th e d i sr 1 .I but ioan o f s hoDr e-bIDrea k er h ei gh ts fo(r a w a ve t ra Ira thI Ienr f rocmf eq u a t i mis r ( 2 4) a nd ( 2 6) 203 10 o LABORATORY DATA FIELD DATA + +]+ + Gaillard (1904) + a Scripps (1945), Leica Type I + v Scripps (1945), Leica Type II x Scripps (1945), Spec. Meas. o Balsillie and Carter (1980) + o0+ x x db o (m) (m) > ,db = 1.28 Hb 0.1- /o� 0.01 0.1 1.0 10 Hb (m) Figure 4. Relationship between the water depth at shore-breaking, db, and the average shore-breaking wave height, Hb (from Balsillie, in manuscript; Scripps data reported by Munk, 1949). 0 10" - 60 1- olMo HHbb(n / b tan aa / 0/ 10 Figure 5. Relationship between the width of the shore-breaking zone, ( andm) tan ab Figure 5. Relationship between the width of the shore-breaking zone, wb, and the average shore-breaking wave height, Hb, and bed slope tan ab' 0.2 0O 0~0 Sb = 0.21 Hb 0 0 0 ) "~0 0 ' 0 0.2 0.4 0.6 0.8 Hb (m) Figure 6. Relationship between the average shore-breaking wave height, Hb, and the standard deviation of the average height, Sb, for single shore-breaking wave trains (from Balsillie and Carter, in manuscript). I 2 I: 3 (dI.- + OA4 b)(u2 lb)1 b~~~~~~~ b b O b~~~~ wh i ch i.,s I r ag reemen t wi 1 h eqi ua t1 i on ('2 5) By- u An - I 96.3) - repor I-E tha t ma ny waves AAAseemo to s 1. i p o v er t1h e b ar ui~ib I olk en-r or wo i t hoau -1 ma k i ng a com ip I e tc b re a k< , A 1 ari that `rdur ir -gthe peak of storm wave acti-vity, it appe..ars that 5K-. p:er cen~Tt of aLL I waves b:reak.' H--e assumecd thiat -the diep: h- over the bar-1 cr-e.,t i s aprximt yequal. to i,)3 1-1b w h enre Hb i s t hef s ig9n i f i c:a n t s h orIe --brYea ke r hei gh A- Whrea sh or e-breakin 1-lb :, A~23 H b bbust rat cir F n igqur e 7 ( from BLa sMI . ie and Carter, 1984) , -then: dbC9 bc Assufi ,I ng t ha t 5 O% of1 t he via v(-s I- o f a s ing b3e via ve -t ra in -,Iel- r at i Ing a 1.ong sh or e b ar s hor e-b reak oiv erI the c r e st a s p 1. u n ge r s t-h e c.:or r e spon)d i rI-g b r ea k er o n (. w i(I citi1 ho-v er t he b ar- c re st Wjbc b ecc o fne:! f r om e. u a tI i o n ( 2 5 ) 0 . 5 H- b 't a I a bs The average po int of sho-re--breaki<1ng is therefore ILocated a distaniceC of O.~25 wbC seawiard of the cr est apex. Hence, us ingj ei.ua-t ion (24): CI bc - i 2~9) I.Ib whi ch. i s c L o se to c) e ua t i onT ( 23 . Th ese sever a L 1. i Ties o f rcea- Co ng s I~].-Uggest, then, that the dlep-th of water overn -the Long.- 24 ./ o ' o / 1.0- 0 Hbx . . A / / H 0.5 - 0 bx 0 (m) ? _ � _ oj � � Hbrms = 1.02 Hb 0.9999 - O AHbs = 1.23 Hb 0.9976 20 ' OH bio = 1.37 Hb 0.9932 0 I I I I 1 I I ! 0 0.5 1.0 Hb (m) Figure 7. Relationship between statistical wave height measures, Hbx, and the average wave height, Hb, for single shore-breaking wave trains; Hbrms is the root-mean-square shore-breaker height, Hbs is the significant shore- breaker height, and Hbl0 is the average of the highest 10% of shore-breaker heights (from Balsillie and Carter, in manuscript). .53hr (4 bar c re . +, ape i e--.J ita. 1. t1o *1 hne a v er-age ~c.?sh )r -e -re a ke r heigh o c: c r r i n ; o ver t he IDa r s Loape e i... , db --I-I). B-3ase(.-d on i t hi e w r< o f 14a t t Js e. (- 1 97 4 z , i 9 7,4b : a iir.Id Br it iu anrd CTunob a 1< ( 1 977) i t I s a f s o pc)s- lb IDL.e t o s-p ec i f y -the tCos.-s -s Lorpe re it r ed toc :r od uc e p L ung i -rg sh or e--b rcea k er N Based on recenit work1 (Ba Ls I IeI, tin press) , moodif ied their resu Lts to suggest: /9tan~c a. bs Iun (9b D., 64 t c. 50, Sp i LL ig (30) >5, 0, S ur g in W h e re bi s t he iemo)d i f ied(i srf s i fj i 1.a r i t y p a r am(e ter Fur t hear, Ba is i [L i e i rin press) f ou-nd an op t i maum p L.ung i -nq va L ite occ urs wher-1e 9 1 -0 ( corr-1-espon)c)d i ngq toc . labou t 7 6: c)f t he t op o f thIe b r e ake(-r c.r e st- c: om fp r i s-i -ng t(h e p 1.i un (1i ng c ar itv .I e Hen c e , a reresn a t yeq stos sioea rc*~ fi rd to(: prod ulcea w L L. for med p Lung er i s g i en by: (tan- abs)req (- Th e d ep th o f t he b ar -1 trog h, d bt jit L a nd wa r o f t~he(- b ar c r estt c-a n a L s c b e i d enrt i f i ed cl Ba s ed con o ve r 1 000 f i e I d anYId L a bo r a t o)ry i ea s utr (i aeen t s ( Ta b i. e - ) , a nd( g i v i ntg e q. it aJ w e~ i Int t o fiefLd anld laboJaratory aver~acie-S (ci nc~e L~abcorialtory dia ta reprresent cond i ti o-ri at the -time of Long shore-bar rfor mation, a L though rc aLi nc err ors., may be i nc Luded), anid where from above dbc I-Ib 26 Table 1. Relationship between the water depth over the longshore bar crest and the bar trough just shoreward of the crest. dbt I. D. Locations/Conditions n db dbc FIELD DATA Lehman (1884)* Pomeranian Coast 4 1.61 Otto (1911).* Pomeranian Coast 5 1.76 Hartnack (1924)* Pomeranian Coast 2 1.82 Evans (1940) Lake Michigan 43 1.45 Shepard (1950) Scripps Pier 276 1.23 California 66 1.63 Oregon and Washington 38 1.93 West Coast U. S. (other) 116 1.63 Cape Cod, Mass. 62 1.47 Hands (.1977) Lake Michigan 162 1.50 Herbich. C1978) Texas 27 1.37 Present Study Florida Lower East Coast (1975) 49 1.64 Panhandle Coast (1973) 43 1.93 Panhandle Coast (1981) 85 1.66 Lower Gulf Coast (1973) 45 1.53 Field Total and Weighted Average 1023 1.50 LABORATORY DATA Keulegan (1948) Initial Slope: 0.0667 16 1.17 0.0333 15 1.72 0.0200 5 1.60 0.0143 9 1.69 Scott (1954) 4 1.89 Laboratory Total and Weighted Average 49 1.73 * Reported by Keulegan (1948). 'Twoc ad c i t 1 o na L I Lo n9s hc r e b ar fme a sur es- a re o f s pe c i a 1. c o - er n 'These are the Iecingth (if they- bar Lee srl.ope, xt, measured from the bar* L~t andw.ard to i ts Compan ion bar trougjh and wh--ere a mu it . t i .-bI-a rr ed nea r shocr e o c cuitrs t he 1.o n gs5h crve b ar .i p a c_- ig bc s mie asuredi-cI fromf baI, r -c: r e st ci ba r -c I e s E i 9 n i f i c:a ntL l~a r ge sa m ITes o If f i e L. d earmnt r :ortciIf, e Evas (1 940)..- an d H-Iands (S i 97 6) f or mu i.t L 1- b a r red n earI- ho res~ a Lc, n g t he ea st er n shIIor e o f Lk e M i c h i q ain- a re p Lott Ae d i n Fi: q itr e s a and 9K Wh I- i L th1-ie 1. ong -is h o re b a rs w e re a pp a renrt 1. y n ot f or mnedc a t t he t i m e t ha t Y i e L cl m e a s ur eme nts w er e mra dea, s uf f i c i e n d a ta a re re1po)r t ed to. Provide averages therebty -reduci-ng -the effects of secondary s ed imantF re-d i.s t r ibuat ion diue -to olthe.-r mod i f y ing Iin f Luen ces- 'he etL.atIosare: X~~4 d7 70 d" 33) bcs ~~~c bc w h er e d an.-1d cl are def i-rned Iin Fi gur e 9 , and "bt 1. ci bc (4 'Th er-e f ore i t i s pocS s i b L e t o p re d ica t t he p i n c p pa L. ph y s ograph I c f ea 1F ure s o f I )n g sh or e sai ndc b a rs i n te r ms o)f i n c i d eint s hore13-br a k< i -rg w avej ch a ra ct er- i ,,-t i . cs 28 300 I 1 I IJ I t I ' i 250 - V 200 - xbcs = 42 dbc Xbcs /v (m) / 1*st to 2nd Bar a O ; ~ /V2nd to 3rd A A loo0- / f /3rd to 4th " 1 100 - A 3 � 4th to 5th t Y V ACb ~ ~ i bcsSWL 50 - , , + , , 0 2 4 6 8 10 d (m) Figure 8. Relationship between the water depth over the bar crest, dbc, and the bar crest spacing, xbcs, for multi-barred profiles (data from Evans, 1940; and Hands, 1976). 80 - y Xbt = 14.4dbc 60 - /XF ! o0 1st bar Xbt (m) oA 2fnd 1o3Z C a a 3rd 40 a /0 0 4th A A 5th m/o / I I I I I I I o 2 4 6 8 dbc (m) Figure 9. Relationship between the water depth over the bar crest, dbc, and the distance to the bar trough landward of the crest, xbt (data from Hands, 1976, points represent averages as indicated in Figure 8). 1s n nq a c:co )un ts su q 9e zt t h a tt h e Lat I. ae hi ght o th e e -f iCeI w a ve( fo cL I1cLow i nc -I -in i t iaL h. lc) e-- -) ..a k i T)g p r ( ar - [y de- p ends o n t lie r at i o o f t he(: w at er deFp t h n o ve t s ubf e-r ed s tr uc. t u re to Clal measUre 0o f t he i inc i d enrt w a ve lI--$e i g h t d C HI (e Ng a ak afur a, .3h i r i a sh i and ,Sras ak i i 9 6 6b ; VIc Na i r and, ,'o r eniis en , -19 70; Su ha ydca a nd ob er ts, 1977 anrd K eadcly anrid Coc L emfa n ,1 9380) However , inr t he p r ec: ed i n se Ct i oni- i t h as b-~e ein s u q g e stAed tih at1 f or n at u r a L towcjn s h c.; re b - s t~m h :ra1 i o d bc ?I1.4b h as ana ve r a ge v a 1. u e o)f unI- i 1 t" Ix h r re I.I b s thei .- s io r e --b r ea k i n (i w av e h e i g hit p ro()d kA r i ng o r inr r nea r e uj 1. ii br Yi u f w i tli -t he b edc -fo rm . W!lh e n api.)p .i e d t o c x i s ti ri n r e t.at i o n sh i p s , cc)n s i s t ency r es uL t s. F: or ecx amfp 1. e t the r e I.a -t i r oslhi p o f S'uah a yd a a nd Robe,?r t, i - yen b y e tu a t ioc)n (5) r e su L ts in H r '1b = 05 6 Th e r en L at i onish i p d e ve Lop ed frT-o f t he d a ta o f N a k< a (ou ra ,h i r a ashI- i a ncld .a sa k i v VPn b y eq. u at i on (1i3) r ks5u t s i TiV Hr 1l1b O 5 4 ( ass-umroIng 1. 1/1 0 =E 1 7 3, wh e re fr-om iii1 e p r ec e d i- ng s eC c) in a nd rcoarp1,o r a -1 n g e :I. u a t ioc n ( 3 2) 1*. C 5 w b 0 2 2 T\Tl-lb , anvid from :3 a Lts-i L 1. ic ( 19314 ) L. b = T _Nf- I go H T ) ThIne r e1. at ilo n s i ip o f Ke(-,a dy a ndc C o emfiianri, ( i yfen b y eq.-- . ua -t i on I23''D re(:~s u L tisF I n -1r / 1-1 053; a n dt- he r-e La -t i c)n sh i p o f J ohniis on , F u chs a nd ( r r i s on y ie .ds Hz11r 'H~ 0 a5 9 ( assu m In g f r om t he a ve r acjed -fieC41.d data of Hands;, I 976, figure 29, flatr iibc = 1 . 37 R where R is the bar rel. Ief w = h 0.5 dbc~ ~_idc d'= hbc +1-ib) T hese r-eLa--- A I o nsh I ps rs L I t i n a n a ve ra ge va tuI.1e c f H-1r /I H 1 C'-1 " r b 5 F"ur1 t h-1er - 1 U udy YshIIo ws5,I 11 VC',howeve t ha t add i t i o na 1. -f a c t orf s a -f f ec t w a ve h e i g Ii t t r a n sm i ss i o n wlthiI c h c an b)e I ci e n -I i f i edc to- -f ur -t her r e f inre thIne p r (.d i c_ i y e r e Ltat i o n sh i p a s i t a pp L ie s t o :3 rna 'FI ura I. L cof I g sho.r e ID a~ r f oeC'' sc C.' un 'Fs h- bc II t -f oc C] u c e dc..i ear T. iI--- i ceIti;e iI u a 'F ; I c:' i II nc.,t a Pp L i c abI i.e fo(Dr n-,a t urI a 1. 1. i t t c:'r a L concij - I dit on a -Id because it1 can eas i Ly be expressed in other terms, thenr T, - Fb) Lb,~ ~ ci c bs, Clbt arnd MOare -the pr inc i pa l factors onr wh ich H"r /H'b shout d be clep end en t Furthermore, the average grain s ize of sed iffent , il, may be c. e~i nina ted s--ince we are dea iming w ith sand, -the va Iue of dbc/FIb is cLose to un it~y, -the Iau of (1' bc /dbt i-s apinrox imate Ly 1 ~6, and -the m'ag-niu %Ftd o.f '-art abs fiust be suiff i clenIt toi Prod uce the wave type nec:es ~arv for I.(ong s'h(or e bari 'for ma 'Fition ancd ma in Fe nanc e TheI r em- fIa i II i -i fac:tcor~s, then. are *T, 1-1 n L.b 'The mfosti baic:-J .I r aining pa~.-rameter i s, -therefore, 'the wave steepness - b/Lb , r (-"4k'i 'va Lent wave steepness ~1b" /( fes no-tted ear Li er, for var ious reasons, -few fieLd data are a va L ab IDL.e t o q.uanIIt i f Y 'hie e ff ec 'F 'FhI: aF tL ongqsh Io r e b-)a rs- hIa ve onI 'Fr a fs for fin i ng i IIc i d enI)t wja ves "r' h erI- e foDr e , th II L e a LI. a va i LabI i. e fie Lci d a t a arI-e u se d inI thIis i nve st igqa t i on, *Fh e da-It a a r e a iugmented by ava i Lab Le Labora tory resiu I.-ts wh ich appear to a pp roxifima *Fe c(Dond it*Fi ons ex h i:i *Fedc by na *Fur a L Ic:ng siior e bDa rs :Basd con conIIs i d er a t i cotIISs set- for 'F t I e ar L.i erv,1 labIDorIa torI-y d a ta s e Icec t ed w e re r eq u i r edk t o me et thIIe 'fo( L I.owjinIIg c:ncjI-)c i *F ionsII I. inc: i d en 'F wa ves shI or c'- e- I rcea I,. c *F) h Ie IDarr i erI c: r e st oDr IDar i- er I s't-ros, s lpe, 06 < d 1bc /"'b -o 4 xe ' hr p1 n type b rcakier_ s were k I w IIw to oc c)r(- urI- c--, r t Ihe : a r r i(-,I er c_ " es't i.- II acl as u in ni II h Ie wav es sh o r e'-'bIDr cea k< as-, p 1. uII ger s *F it I e C. itc h-1 Jcl own po i IIt was a Lways iLavclward of -the barr i er creS'F apey A I. 1. c:ocnII- ci i *F i ons were *F es'F ed numer i c:a I Ly where pho'Fogr a ph i c ev i ci ence was 32 " Table 2. Field and laboratory data for wave height transmission over bar-type submerged barriers. dbc Hr. Hb dbt I. D. tan a Hb b g T bc FIELD DATA -- all natural, sandy beaches. Wood (1970,1971) 1.250 0.45 0.00349 0.0556 Sp 2.400 Dette (1980) stormwaves --- 0.55 0.00567 0.012 Sp** --- Balsillie and Carter (1980) 1.505 0.451 0.00108 0.0011 Sp/P1 6.471 1.072 0.288 0.00170 0.0017 Sp 1.979 1.026 0.360 0.00222 0.0509 Sp 1.233 1.101 0.229 0.00193 0.0968 Sp/Pl 1.491 1.344 0.284 0.00055 0.0375 P1 2.042 1.143 0.650 0.00990 --- Sp --- LABORATORY DATA -- all fixed beds. Hall (1939) 0.689* 0.390 0.00110 0.6667 Su** 11.000 0.981* 0.356 0.00183 " Su** 6.000 0.771* 0.470 0.00399 Pl** 6.000' 0.801* 0.740 0.00758 " PI** 6.000 1.197* 0.245 0.00190 " Su** 4.333 1.252* 0.537 0.00396 " PI** 4.333 1.117* 0.816 0.00815 " Pl** 4.333 1.275* 0.433 0.00648 " P1** 3.000 0.926* 0.423 0.00208 " Su** 6.000 0.825* 0.437 0.00382 " PI** 6.000 0.693* 0.598 0.00796 " PI** 6.000 1.069* 0.392 0.00453 " PI** 4.333 1.044* 0.641 0.00844 " Pl** 4.333 1.128* 0.361 0.00165 " Su** 6.000 0.665* 0.308 0.00497 " PI** 6.000 0.748* 0.551 0.00481 " Pl** 6.000 1.236* 0.445 0.00465 " PI** 4.333 1.364* 0.770 0.00646 " PI** 4.333 1.389* 0.424 0.00554 " Pl** 3.000 0.694* 0.504 0.00465 " Pl** 6.000 1.012* 0.414 0.00467 " Su** 4.333 1.126* 0.780 0.00783 " Pl** 4.333 Mason and Keulegan (1944) 1.579 0.223 0.00023 Step ---- 1.000 Putnam (1945) 1.153 0.558 0.00551 0.425 P1 1.000 1.177 0.502 0.00426 " PI 1.000 1.119 0.385 0.00227 " P1 1.000 Table 2. (cont.) tan bt 1. D. dbc Hb g T2 an abs D H dbt Morison (1949) 1.459* 0.750 0.01560 Step P1 2.665 1.490* 0.663 0.01560 P1 1.598 0.726* 0.548 0.01560 " P1 5.344 0.752* 0.471 0.01560 " P1 5.166 1.130* 0.725 0.00597 " PI 2.754 1.130* 0.629 0.00597 " P1 2.754 1.155* 0.643 0.00597 " P1 2.294 0.600* 0,500 0.00597 P 5.294 0.602* 0.488 0.00597 " P 5.166 0.905* 0.692 0.01153 " PI 5.347 0.927* 0.619 0.01153 " PI 5.166 0.817* 0.562 0.00756 " PI 2.431 McNair and Sorensen (1970) 0.875* 0.297 0.00294 0.1000 PI** 7.000 0.784* 0.389 0.00206 " Su** 4.000 0.870* 0.458 0.00214 " Su** 4.000 0.812* 0.379 0.00387 " PI** 4.000 0.942* 0.468 0.00451 " PI** 4.000- 1.093* 0.510 0.00585 " PI** 4.000 0.941*. 0.483 0.00633 " PI** 4.000 0.947* 0.518 0.01009 " PI** 4.000 1.142* 0.605 0.00711 " Pl** 2.800 1.088* 0.589 0.00500 " PI** 2.800 0.775* 0.375 0.00452 " PI** 2.800 Sutherland, Sharma and 1.171* 0.389 0.00427 0.1038 PI** 2.000 Shemdin (1976) 0.801* 0.571 0.00624 " PI** 2.000 1.096* 0.535 0.00532 " P1** 1.667 Battjes and Janssen (1978) 0.84 0.43 0.00410 0.0500 PI** 1.917 Keady and Coleman (1980) 0.952* 0.489 0.00627 0.1493 P1 3.000 0.783* 0.475 0.00529 " P1 3.000 1.169* 0.649 0.01197 " P1 2.333 1.051* 0.624 0.00851 " P1 2.333 1.082* 0.642 0.00575 " P1 2.333 1.027* 0.575 0.00403 " PI 3.000 1.354* 0.758 0.00813 " P1 2.000 Breaker heights predicted (see text); ** Shore-breaker type predicted using method of Battjes (see text). inot ,- ava i L ab 1. e. he a cc e p t ab Le d a ta a re I. i s t edc i n T a b c.2 and? ep n t~~ a b o t t cl E. o f the i7 v a i a 1:- L e L ab1 o r a tc)r -- r es A Lk s *for. e dr13 a dIbarr i e r s E xp ress o -n aof w ave hec. q. jht t ransm i ssw iocn iw Li rm i -ted -to t he(- Aiho r e-- br e a 1, i n-Ig w a ve h e i yh I - o c u r -I m o ve(-,r theo b a rr i er -, and- I: h e - r-.e fo - me apd wav I v9hc, i g qh t ,H r The H bmeasur e i s used r athIier than H--l -the incident wave he irgh-t repr esen-rt ing the s,-tab Ie Coast- nrg wave trave Li nc ove-lr thre constant dep-th Port ion of the l.abora tor~y channireL -near the-- .tr uc ture toe. : t- is known -that w~avyes peak d<cur inig the sho-re-br -eak<i ng p-cocess on who A.I-.li ng EL opes anl-d th-at- H b is- C:'ft en s i gn ificant .y g;rea-ter ii- nva L u(- tha---n H1- ( -13a I. si [L Li e 1 ?-3380, -1 983b) Tine p ea k i n igi me r:hIIani iSmf i S iI. LUs t r.a ted i n F i 'q urI e -1 0 , wfh e re t he w a ve und e r qo e he I- e gh -t a t t e nua t i onr a(: r o s t he s;hc)a L.i n g 1.3 Lp e u n t i 1, j usAt b e foare shoe-beakI n ,thle wave sudd en Iy peal.,,A- up ( terfited. a Lp ha wave pea 1< ncj *denoted as~ a p The process i s nion- Li-near. F'ur * her s iA t he0 sho fr.e -- b rea k i rg av e tye t ha t is u7 i1 t i mIa te L.y r e s-p oni- s efo~r prod uclii T yI.oyhre brs hefr e , it Is subm it ted t hat H11 i s a p o orY w a ve lie i g h t fo ca s urI-e Ito u se i n' a .s ;e ss i ny w av%,e t rI a n s ros i s- o n o v er ~:5. ubmIe r e d b a r r i ~ e v ::'(-j rt In i s r eason,-c -, wh e e l~b ~ .usare Tiot re[' e I b i s ci e term ined us1i ng t lie:- f o .L cjkgw Ing r e 1a t i ons- -hi p Hb/ dP-vp I o p ed 1-.) - B a LwA, i L L ie (1 983b ) and i .luwr di n F igure. 1 1 The data of Tab-.Le 2 a-re p Lot ted i rr F igcure 12.. H evr b.)e fo)r e the1(.. f orm oI cf t-h e e .:Lua I i o n re(:,,pr esAzent I ny, -th e d a ta C.-a n b e 3 3 1.2 ----Constant Depth -- tan a t 0.054 l, ---Deep Water - = 0.00963 ,I~~~~ ~ ~~~~.I- Hi T2 - -':0.0110 gT2 =0.00887 19T Direction of Wave 00o , Trove I -1.2 1.0 - I _ H -- I Hm 0.89- IN - 1 ~~~~~~~a0.9 - Corrected N00 ' -.% Data from Putnam (1945) ll T- 0.965 s. d db 1.28 -0.9 0.7 10 9 8 7 6 5 4 3 2 d/H Figure 10. Illustration of the alpha wave peaking process during shore-breaking, denoted as ap, where Hm is the wave height in the constant depth portion of the wave channel, and H. is the wave height at the initiation of alpha wave peaking (from Balsillie, in manuscript). 2.5 i i I I I I tan ab _ � 0.025 O -_ O 0.0292 2.0- � 0.050 _ zA 0.054 H b - 0.0556 Hi 00.072 0 i - 0.10 ogk 1.5 - V 0.20 1.5 - * step V 4 H; - 1-0 - 0-4 In tanh 00 1.0 -o |j 1 1 I J I I I 102 - 10 Figure 11. Relationship for prediction of the shore-breaker height from the initial equivalent wave steepness parameter illustrated in Figure 10 (from Balsillie, in manuscript). FIELD DATA LABORATORY DATA O Plunging; observed A Plunging; observed o Spilling; observed A " predicted 1.0 - " predicted V Unknown 0.8- A , 0f a P ~--A~OA 0.6 - Aj Hr . A A A Hb . Hb A A 0.4A A Hr tanh 175 0.2 - = 0.26e gT2 Hb 0 0.002 0.004 0.00I I I I I I I I I I I I I I 0 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0,016 Hb Figure 12. Relative reformed wave height, Hr/Hb, versus the equivalent shore-breaking wave steepness parameter, Hb/(g T2), where Hr is the reformed wave height, Hb is the shore-breaking wave height occurring over the barrier crest and T is the barrier-incident wave period. d: i tr oInd , som IIe g u ci a nIc e c oc-,-Ii: e r nI i nIg o I.-ower andI . uIDpper (II i t s i r -.IIii.1 red C. C)n C: v rnI i II g t h e 1. o w er 1. i mn i t ,t h e -.1.u es I i C)n a r i s- s i f th11e e q. u at i onI p a sses t h rough I t he o r i g i n o.,f thIIe p- 1. ojt o)r i II t er -- s ec t s thIIe o rd i n a te a t s omfle p os it i ve v a 1. u e? F ir st ,i -1 i s toa b e r e con IIc L led t II t Hr/H r Illp- r c -e senIt s a rea f.s ol. ut -io I o, anIId -1 h at1-b c annoI-,I t g o t o z er O sin Ce t he v a1.u e o f I-1 r 1- b 'ot Ld1.e no-s I-~-enIIs ic a L . e v en- if H r goeP.s toa z er o ( wh i c:h itIw OL d) Second, it is possibLe for T to be L~arge, thereby producing a s wa 1. . v a i. u e o /F Hb g 12) .. :1:n f a c Ij j: i f (D ( e iEdea 1. j I n w iI- th S o 1. i t ar y w a e Fl T 12) woc)u l. d e s se It i a 1. 1. y be(: z eo and) .i Ic a Pcs. t i y e yII-tO itr c p Pv a 1. uec. woc)u L.d I--c;u. 1. I . V i s ua 1. inspelact i onI o:f the data of Fig ure 12 suggests lbhat where Hb( T2) = O Hr /Hb wo dhave a va i.ue s.-ofrewhere in the rancie of fr om -,0.2 -to 0..3. Hen-ce, a transcendenta I power curve fun1.ct ion is el.i mi na ted as a form of t~he represent ing eq:ua tion. Arn urpper L.iri it abs issca. va I.ue may be est i fma ted for fo:rced wave co()n d i t ionms . M i c:h I. eI ( I S 9 3> f ound-,c th[Ia t thIIe L i mit i rI-g c r f e - i onI f or- t he st1a b i L.i t y o f w a ves inI d e ep w a I erI- i s g i v enr b y ( H/L)Ma "1 /7.. Where from Airy wave thoyI0= g T 2/ 2 then HOZ(g T2) =. 0.,O'217 ., Notinjg that H0. and Hb are eIo eq u i v a L enIt anid that for p L ung i ng shore--brea kers Hb (c""-ld very we Ll. be greater -than H., then iwhere on the average H'b 1 .~3 H-0 (BalIsiLIL ie, 19BE,, assuming H0) = Hli) , -the ratio may be given as F.1~ 2> = 0.0175., ApnLying these vaI. ues as giu ideL.i nes to the da-ta o:,f Figur-e 12, appears to~ id:ent i fy -the upper L.i mit of val~ues~- for t-he abs i-lS-ca . V isualI. ins,_pect ion of -thei data Suqg(-_._'ts that -the valIue of H r /H b fmay a sy mptote a j a bc'u.t 0 .. 7 for about 0.014< /( T 2) < (.01-)6., 38 Th 1. , eq. u a 'I: i T::z f i t 1 C. d to -thd ia t a i f s h f thet r a n s'c: e.,?n-' C! en-1t a 1. e x 1-,on en rl a. -f orm(- y i c~ I.d i n t a -n ti 7 5 2 r - O~~026 e (36) Equat ion (36) is fitted pr imar iLy -to those dlata where the p Lung ing Shore-brealker *lype was U-nown to o~:u To some extent, the Laboratory recsulI ts of Mci-mi son (1949) diet ermi-ne- wher dhesi ~Igrn curvec- a symp tot es. Hi I sresuLtls *for h i h wave stleeprne~s- va .ues, a f ficc t inq Athe eq~ua ti on, ncc: c uf or two va L ucis , a.J Hib/0 'r i--j iI nd for fojur va l ueg at I.I"I/(q T2 ELO() 01 6 . l:n Large part, Mor ison's res~ul.ts for high wave steepness vaI. ues ref Lec t the i f.uneof barr ier width, but do -not represent the effects of a bar st os~s s Lope--. lt pciss i b e -that t he asvmpo t Ic: vaI. ue i s somewhat diifferent tha-n shown and fur 1 her reerhappears warren--tedci. E-ven EC), eq:!ua-- t ion, (3)-apasto prov ide a r''~tant a rfi-nemenrt i-n the des i gn so I ut io-n for L~oncishore bar s. WME: p.i:E PEK14"'01-1TTENUAI rrON lt is ge-neraL Ly viewed -that asc Lo-ng as shoaI. i nc waves- are undr g i ~:irefr ac:t ion, -the wave perI oi is cons-erved . Howe..ver from much of -the ex ist ing L~a boratory r e earc.cii i tIs reportedc t ha 1 even ---re ho cb reak1<ing waves r eforfii, the wave per iod r emairns c~onser vc-d Predci ca ted on- -the ob~serva ti on that.. the f unciementa L refc)r -mec wave c:r est has,-- a p~er iod ej. u iva i.ent fio the i nc id(-ent shore-brea 1<ii-g wave.. irn some cases- -th is appears to 1:1e a f unct io orcif p rob Lems i n nca suri-ig -cthe r efor med wave 39 c h a ra c tr i st I c: ( eg .,c a I - rad *Sor er--Isse n , '1 979) o r F4 d e 'f I -ini - t I ye r e s .i L tsar a T-eo I s e rv ed( i ri t he -f i e [c d Byrc ne C 9 9616) r epI)o rt-s a 'n0%"" -r-ed tc: -t i onT- i -I the-[ .- r e f or mIe d w a v ae pr i o d foc [LoL(w i inyI bar -I n -c i d e -nc e fc)r -n o -n -bDr ea k Ini Ygw a ve s Car ter an~d BaIs i [tIie (1933) rep~ort -that iq-gn i-f Ica..nt wave pe~r i od r ed uc- t i on c an--( oc cur -foIlow 1vi 1ri g sh or e-bDr ea k i nct; o ve(:r Lto r ngso r e IDa rs.5 u ha y da a nd R obIDert1s (19 77) f o u nd I tha t thIne a ver a ge w a ve p er i o d sho-I)r e wa rd o f r e e fs o v e r w h i ch IDbr-ea k<1 ri g aoc:c ur redc weP.re .smf atiLe r b ny ahIo"c)t t 5 0%'X t o 7.5% t han - It-he(: o -f fsh or -i( i--e wita v e c per i o d s Howe iv er th1-;e p.-,a uic i t y oj f f i e [ci d da t a dloes- not - a [Lowc)t f orth e d ev e t.opImIIe n t o f a P r' ed I c: t i on r m e 'Ib o d n r -the- ( e x 't e ns i y e L ab o rat.1o ry s t udcy o f ikla k< a mtu r a , h i r i a shI anrid S a sa k1< I -1 9 66 a I '1 96 6b ) w4a ve per -f-i o d a -t teniu a -t i onr d ue -tocI br eak irg was -reported., Re[at Ioinsh Ips dleter-minied by the a uthor for the. dlata .,.. eqiuat ioins ('M) and ('17)4..4 can biIDe t ra n s fo(-,rmte d toc repIDr e senrit c on rI t i - onris a t sh o r a-b--I r e a k i -ng JA i er-- e from Ary wave 't 1-jeoy.) r T 2 1/u.i, anid db = J.2 141 k &:i(a I on(I ) IDe :cD ome.,, O .. 4 4 Tr Hb1 - ~~~" ~tanhn 256 2t 3 for aI sm Io ot-h .i-in ne ar- slo p e aof tan 0.r1 a ridc 0.1~~~~~~~~~~~~~~~~~~~~3,1 F~~~~~b 6 ~ ~ ~ b e. 1 u a t i on~ r ( 33)D bec o me ir 4 C' Tr ( T )9 f ;q-1-hC . csoe b a rs 'Zo me -f i e l. d d a ta f r emi- I~y rnre ( 1 9 6 6) W o od (19f7 0, 1 9`71:)C r ct er a nd BEca 1..si~ L . i e (9 833) a nd anT a dd i t i o na 1. pcoi nt co 1. L ec ted b Y t he a -t h or , and some L abor a t ry d a ta fr Om Ma son, anrd K eu 1. eq an (19.44) a re p 1.oI t ted i n Fl g j) (.- I 13j a L ong wmi th eq ua - io)n s ( 37) a nd (39) I isA app)ina renet fr Om t he -f j ur e t h at s *T -'I- e j r, t h d at a i s on A- i d er ab- 1. e, a I. th oitgh t-h e dat. Ia 'fa L L. iw i 'F h i -n -F h e env e Lope d e scrr i b e d b Y e ci ua t i C.ensF ( 3j7) a nd (39 ) :19 I v ie wc: - th e pr- eb Iems en C o un t dr di -I-other I. a b: or- a For y At u d i e.s i t isF unifr Ol1 u-na te thatf Na k a mra , h i r i ash i and Sasa 1< i d i d nc t e L a b or a te o n t he i r mnetIh od (5s) o f m ea s ir e (se rt1 o f r etor ed( la ave :h a rac(- -t er i A;t i c s Wh i L e a (1d di t i ena L Stitud Y on w a ve p er i o d t ra nA- (Irforma I. i o.1n o ve(:r b ar-ty pe f ea I t ar es i s wa rrent ed ,eq.I i a *t i on ( 34) p)r c v i d es t he o n L Y ex iA s-F i n9 -f or mna 1. i z a t i o n p r es,,ent I- y a va -.i i at b c :: t - o s b e n ote-d ,ho wev c.r F, h-,a *F ei. ita t- i o n ( 39) do()e s c: o n -fo)rmi t o re(-p or-t ed f ie1. d re(:s tL t s WAVE I..J:'NI~eTH ATEu~: Ava i .ab Ie f ieId data (Wood, -1970, 1971;- <:j d and Co Ieffan, -193-:0) ver iflies the signi-f icant reductiF ion i-n wave Lencj th fol. L ow irig shore--break ing over I. cngshore bars. A w i th the wave per le:jd , tsherie i s i isf C c Pen1-F f iel.~Id d at a o 1 I.In whi (::h- t o b ase a p r ed i c FI y ve r e La FI ions h i p ,Ho we ver , wa v e L engt--h a t -F encia t i onl ha Se: Y, vd :o ns fi ( de ra 1-.) e a IF t e nt i o -6 i n 1. aIb :-,ra t )r Y stud j es (Ma s on.-i an d K e i .(" q ea n, 1 9 4-4 N aka (ftr a , El- i r i a f:h-- i , and) Sa sali -1O6 6 a, i 9 6b6 ) E,-Eq. u a t i ons 3 i (2 ) a n d ( 1 B) h a ve b-ie e n f i IFted 4 1 LABORATORY DATA FIELD DATA A Mason and Keulegan (1944) B yrne (1966) * Wood (19710. 1971) * Balsillie and Carter (1980) 0.44 Tr 1anh 256jr-~ 0~~~~~~~~~~-~ IP II II ~~~~~~~0.00 0.01 N B ~ H T P~~~~~~~~~~~~~ 0iue1.Rltosis o.rdcino4h rfre aeproT by, the a tithIio r Ato ...~e men t a.i1 Li dta wh i c h represent a i. i nea r s Loc)pep, stJ-epI- s L.o pe., anid u sbtme rg9ed b arrT i e r s .IJs I -119 de veC I.oap ru1e nt- a pp L i e d I ri t he p r ey i o u swe c:t I on r eq-. uxaIt i on C 1 2 ) , (8) anid (13) are., transformed to c~ond it iO-ils at shore-break ing , -to yield: O 2. -1 4j /~~~~ b ta nh 8 05 2IL f or a Li ne a rL s Lp e o f t anr a b= fo)r a step prof i Le, anid 0. ~~~ r> jO.,45 A s w i t h t he wavNse p e r iocd, -f i ea. d a ta ne ed t o b e ob L)ta i ne d t o t e st * ~ ~~ the L ab o)r a t o ry d e r i v ed r- e: L.a t i o nsFh ii' . In tIlhe i vi t e r i ma , eqL u a t i o)n 4 2) i s t1h e o n Lv'y a va i L ab1 L e p re d i cat i; ye r e L at I osh In p POST- BAR BEAK INGc D'I.STANCE MEA SURFv3 Det ai s- of wave he igh t at t enm-ua n otoLLowi-ng shtore_- breaki rghave bee inves~t iga ted for shore~,-break inrg waves ont Li ilear pr o-fiLe-s (1--or ikama and K<uS), 1966,; I<lithi and Sask i, 1966; Boweil, 'E'rimnar anrd i mmon s , -1968; Nakamura , S i ritash I aind S'ask i 43 0.214 L Hb Lb tanh 805 2 L~b gTh33b2o'03 0.38 Lr_ /H 0.5 [ tanh 3.39 Lb gT 0.45 0.8 -�r0. r ~~~~~~~~~~~L h Lb 0.6 - rff 104 0.2 - 0 11 1 I I 0 001 001 Hb gT2 Figure 14. Relationships for prediction of the reformed wave length, Lr- i 966a arid .5 i nrj amiset t i an-rd W ind , i 91,--31, a ndl on s tei::- t ' p ep ro-.- f i Ie~s ( Put-namn 1 94~5; Ilor i luit aa an -ic Kuo 1 9656;jr cl Sd ~a Ia ra i a nd I woa t a , -1 974) j ow e ver , no .- s uc a -- d et a i 1. s a re a v a i Lab5 L e fo w av es whi i hi s h or e-b.r e a k o n L on 9shPo r e b)a r--t y pe f ea tu res N e ver -t he -- s- ~ , i T n te ab10sent.. r e o f d et a i L ed r e s u t s, t h ere i s a n ee(~d t o have know ledg.e of certain post bar Ibreak i-rn wave transforima tion m i I. es tones. Cr 1 t 1 c a L. H i L es.t ones a re t he d is51atance t o t h ba r tro ugh, and the point of wave re-.format ion., It is t.i k.e Ly -that the d i stance to wave reformat ion doesr: not coinrc ide prec isel~ ii..ith -the distaince to the moax imum dkepth of the bar 1 r ougjhi, x bt I (n eas u rc. *fr o m t he bar 1-.) r e a 1, i n P0 n j In :r n f a ct, thIner e i s n o pr e sent L y av%/a i 1. ab L.e p r e.~d i c t i y e m ea surY-e o f Xbt s u i*t.a b L e f or p h ot ct1y p e (:conrd i t i onos- r0 n u mb er ofT r e L a t e d meo.a sur es, moay. h o we v er, be emfap Lo y ed t o a t temnp t t o i de n tf y a L eas_-t e.:[u i voca I. d i s t anrce., P. moinlimum mareof x tm ight b( . gv:n b:y Xtd 'the d is tarnc e from sh or e--brea 11ng over -th e b:ar c--rest to~ -the Ino i n wnrethe c-ur L of -the p .-i.ungji ng wave touches dlown on to the wa teir A-.ur facefro nti ng the wave c rest. O-n a h-or izontaLI bed, whi ichi 5app~rox ima te I.',' app L i c ab I. e t o ba r -hr ea 1< i ng , Ca Lv in (1969) sug *.;sts: 4td 4 1- 4 and w he.~r e x5 i s t he hoajr i z o n A a I. d i s ta n ce f r om -s h or ec- br e a k i -n t o th e e n d o f t hi e sp L ash p o i -nt Wle ishiar and 'Byr-ne (19'78) s~ugiqe st -that 44*f* the va I.ue of xtd from~ -f iel.d data may be more near Ly givyen by: xtd 5,. 6 H (45 Art average of e.:ua t i ons (43) and(- (45) yIi eLds a ~'ok i ng f orm, o) f It-he e 1 u a t i o n asAz xtd = 1-1 (46) S a a ra q i a nd ' tw a tai ( 19 7 4) i n vest I i ya t ed ;1.. hr e - b r a I., n g w~ja ve a c.t i v i t y o n a stIe p- -ty pe p r of i I. c? giv en b y cq. uta t ions (19) -through- (22) ., T h~ e 1 u a t i o n A maiay b e a szsesse:?d at-i sh ore -- break i-nq by e~ua tinyg eq~ua tions (19) a-nd (46), Sett i n tip a pr opoi' t ional iity and read just ing eq ua ti ons (20) through (2-2) to yieIcld: 9.2 1- (.48) a n di Ma b where xa i s -thed ci stance meincsured from sh- or cb r e a 1< i nyg t o th e poc in twhere a Ir b ubb Les d isappe~-ar *from the water c:o . umi'l Na kamur a, Sh ir iash i and Tasak1<i ( 1966a ) found that for un iform -nearsA~hore sLopes- Less than about 0.A 2 to 0.,03, there for ma t ion di stance incasired from, the Shiore-brcaki.~ng p osIt ion may begi ven b:-y eq:.tia t ion (1 0). Us ing Ktomia r anid ya ug han's (1 972 d eve Lop me-nt wh ic h r elat es the shore-break i n wave h--e i ght to thie unre-frac ted deep water wave he i h t givyen by: 4 5 Hb~~~ (150 H0 a n d a s si-Um i -,-i for c: edS sto rm w a ve c or i d: o n s whInere a cocar ci i n; toa M i (Th In, . L. ( 1 9 3) (H0/L0 )m ax :::I ' 11e ,', h C~ = I , N14b In Cl U t iOn1- (in) becomes: xr = 32 Hb (51 wh In cI i s (: Lcosi~ Ato e q.t- uat i o n ( 49) W he re e qi u a t i o n ( 50O) a y b e resst a t ed a s / 0.25 H b o ~ ~~~~~~ 2 a form of eq.:ua t i on ( i 0) accounti i nj -f'or a Li. Lwave steepness, may be g iven by: O'25 Xr ELua t ion (50) or s i mi Lar -~forms :ieve Loped by Munik 1 9491) or Van Darn ( 19"78) c an b~e used to. t ransformr equa t ions (i19 ) -throuq h (22), a lthough severa L prob Lems occUr : i it i s d i f f i cII L t- t o a s scs s t-h e v a L. u o f thIne L o ca . w a ve L e n th 1 L~ i In eel u a -t i ons11 ( 19) thInroau gh ( 22) 2. where i t is assumied L.r L_., the tr ansformed eq.u a tk i o ns Y i 1 . di r e s it L t : les s thInan f or o t her.. - e i u a t i o ns d e v(-- 1 ID od n thi s et: t i onad . i t i s n;o t k n own i f- Komar and Gaugihan' eq. u a t i o n i s a I:>I L i c: a b L e t o s te p - -typIDe pro -f i L es 'Th a t the k: v a L. a F. Of Xr de-.creases with a decrease in Hb(i T 2) does not, at- thi-s! t ime, appaear to b~e pr ohI. ema t ic Hlowever , b ec ause suc~h tr anr-' 46 foar m a ti ci n:: j r, I ro)d u c: e a dd i t i o na 1. c om(np I ex it e s a nd p e nd I nq f ur t h er i n ve st i a t icln, r eL ia n ce i s p La ce i n t he m or e s fit p Le a nd .s r a i g h t-fc or wa rd d v e Lclp fne n ts ~ .e t o f eq. u at ic)n s a re n ow a v-a i L ab L e f roCm wh ch to "br ac ke t" t he Lo()c a 1 i on o)f t he b a r troau q h We know -that the bar trough Pos i tion shou I.d be Less than- -the re-formatio-n diE tance, but greater than -the distani-ce where the p .u-n i ng vor tex reaches the bed, i e., xr > x > x In fact-, the spLash d istance ma.-y be a good1 measure o-f the Loca tion of the deepest Part of the-~ bar trough, sinice i -t approx imates the Loca tion where -the t urb uLence.u Wa s~ hi te eq.ua ti ons (44) and C 48) are c lose, -there is a need to a-.ccount for the add it io-naL water dep-th character i z ing the Lonigshore bar tough mnorpholAogy.. A propor ti ona Li ty of existing eq:Luat ions, yieLds: x bt ij4 .7 H ( 54) whI i c h i s c Lose toc p h Ys i aogr a ph i c aL L Y b a se c e -. ua t ioc)n ( 34A) 1.q u a t i o n (51 ) focir t he d i s t an(:ce t o wma ve re foir mat i on i I 232 Le ss thIia n ph Ys i ogr a ph i c a .L LY b a sed e -:Lu a t o )n ( 33) fc)r Loan gs hor e b ar c:re-,s t s;p a c i ng 9 T h is a p pea rs t o pr o vi de c or rotbo ra t i n q v i d en c e, s i n c e t he w a ve re f or ma ti on d i st .anic e foc)r mnu L ti --b a rre d -near shores wou Ld tie requ ired to he Less th-an thre bar c rest spaci ng If re-formed waves are pri-imar i Ly res-pany L o secondary L.ongsh ore bar formnat ion. C'L C) S U FI tlat1u ra . L i t toara L p r of i Ic es c an b e dclef m iedc i n t erm ojn )f c ompn1-)I Le x i ty olif sh a pe Sil mp Le geometry may be def i ned by a power 4 7 c Lurv~,e funrc t i on.. r ep r ee .?n t i nY- a smi]o o th1 p r of i I.e s h ape Ela secd o n t he(!"C wr k C)of DecanI (i9 7 7 ) , t he(,s e p)roc)f i L e j a re c:o ns i d ere-ad to-. b e ai ~ssgoc i a t e d w i t h i;p i L ii -ng *--t y pe s h or e --br-e a kerI-s a ndc r ep r,- e sent- L on~--teirm, aver age -nearshore prof i ILe geomiet ry. The mi-ost c om-- p e x g e omfe t r y i s e n C:oaunT)t ,?I-erd wh e re t he p ro)f i L .: is.- ch a ra c:t er i z.e d b y L con 9s hor e ba r s, w h ich a re ge nevra t ed b y p L.u ng in -ty pe s ho r e- b rea k er s Th e ge n era t ion aof b a r red p r of i L es i s, a s con-Ie c.-an- i mea g inci hi g h Iy ::omp I. e x I n th I is wor k , h owe.v er , t he I. ong sIhcor e b ar i s pr .e en t aniid i t s ef f e ct o n w a ve r e fcr ma t i on11, o n ce thPIe w a ve h av .~ shoroen --nc the.. l:a r crest , has been irlnves ti ga ted. The he ig~ht of thie reformed wave i s given by eqj.ua t ion (36) , reformedl per. I i o d b y eq. u a I i con ( 39 a I, ad r e f ormned wja ve Le n gt h b y eq: Lia t i o n 42) I n adcld i t i on ,. cer t a i n p o st -I:1.a r--b r eak1j i ng c r i t i c:a L. d is tan c e measrir es, such asl d istance to t1, e b:a r trough and the po i-nt1 of wia ve re-form at i ont, a re i nivest i g a ted. C M ucah a dd i A i on.-1a 1. w 4or -C1< s r e 4 u i r ed t-o q Li auant i f.,y thine e ff e ct o f th[Ie w a ve.s on-- t he s t r uc t ure- ie L Lon g shIo r e b ar g en (-~ a t i on ,- How e ver , b-~y i nIv es-nt i g a t i n thle e ffect* of the s-t-ruc *Fur e on the waves :l, thle 'endc'-member` a sp ecat o f I. co n gs horeP b arI f or mat i oIn , h1a s b e en ad d r es sed RE 1: E. RE N CE S Bea i s i ii Li e , J lI - In Pr e ss, Rede fi n i tio cmo)f sh or e--sr e a ker c- t La ss- i f i c. a I i o n a s a ii u me r i c a i. c: o:)n t i n u umfi a nd a d es i g n- ho)r e ---b r ea k er :s u.b fi * t t e d t o L.. i t t orI-a 1.i a , 2,12 p B al L si1.L i e J H 1-1 ,1 9 84 , kia ve Le(-n g tIh a n d wta ve cc .. L er i t y d Lir j ,I sh or e--br ea 1k i -ng F L.or i ci a Dep art" ment- o f N at1 u ra 1. Res;ouri c e5 B ea c If . (.s- an)Id E h o r es Tec h n i C a., L a nd D1e - i 3 -n M moasr aIn d LI m No 34 --1 ,17 p .48 B a I S i F. L i e J ., Ii.., , 9 8 3 b ,ThIe t ranrs for m- (Ia t i on oF theI - w aN ye hI e i 9 h t cl u r i nIg shIIo re-- br-e ak i II -th~ a 1. p Iha wia ve p ea -,1 ng prcces ws F L or i d a D)epi.)arI-t me njt of N at u a 1. esO'. u- e1 BeIaches a nd0 S o r es Teci c a -I. n e i r n 1eo.ndunN 83--4 33P Ba s; i 1. L i e J I- , 1- 983 a On th1-ie d etier ff I nat i on oIlf w h en wa ve s b. rcea k< F nI r ha I. Loc)w waFjt er :F 1. o r i d a 1)e p a r it m en t C., f Na~.lt u r a R e so urc.e s, B ea cIIe s anIId S'hior e.s Te ch II c a I. andr. 1 Des i F- Memorandum No.. 83--3, 25 p., Ba Ls i L~iFe, J. H. , 51930 * The peak<i ng of waves accompanying shore-c-b rea kiFrig: Pr oce ed ing s of a Sposiunon Shore1.i nes- Passt anid Present, Depar tment of Geo iogy, I'Lor ida Stlate University, Tati~ahassee, P. 183--247. B a I s i LI.i e , -Jl H, and Carter, W .. GA. , 9180 , On t-he r un-up r es u . ti ng from shore--br eakiri g wavte act iv i1y : Proc)e c nc(Ji -r s5 of a .5Ymp os iur onSoeil e Past and PrYesFen-t, De.-p a rtfmen t of C oLg .o i aeUn F ver s ityv, Tai.l al-I assc, p . 29A51- 34 2. Bats-i I.1. i e J., P1..aIIc, and I Cate r, P. , W. C.. 19384, ObsnArer v ed wiav e d a t a: thIIe s II ,I or- e--b r a I, er -I e igPh t1: I. o)r i da D e ry art itme n t o: f N at- u ra I R es o urces ,B e achIIes and c EI Sor--es Temc I Iin Ca L a i . and D es i gn-I M e mo ranId um Noc 34 2, 70 p BatA ties, J . 1A.. , 1 974a , Eur f s i mI i i ar i ty -P-rocewec i Inqs off -the i14th Cc'a s t a i Enic F -neer i nqi Coni f er enc: c :I ca p ., 26 , P 4 677--479 Da tt1Js J. A. , -19 7 4bI. Com itp uti a t i onI o f set ~-1up , L on--g shore) - .. c: uir r enIts r- un-- --up Pan-i-Id o v ertop cPP i ngj d u e t o wa ;FI nd enerI-a t ed w a ve(~s Cor c)( I unI i c: a t i onrls cn II -ly di T a u t i c s D )e 1. f t UnI i -v ers i t y co f Te chI nO- iogy, Rei-c:2rt 74--2, Ra tt .jes , J.,A and Janssen, .) V P., F~ M,.., 1 973, Enrergy Loss and set -up ci ue to br eakiFng of waves : F'roceedi n-A-ivs o:f -the 1 6-Sth Coast aL Ein i neezri-ric Conferenice, chap ., 32, p~ .569 58.. Ben i ama inII, T., El anIId F e i r , J * E~ i 1967, 'The di sin t e gra t i onI o f wave h-a ins on deep water- : Journa i cf FI. ui ci Mechan ics, V. 27, pt.0 3, p.~ 41"7 -430, :Boten, A., J , Drnman, D. L. , and Simmons, V.. P.., 1968, Wave ' set d~own' and set -up : JournalI. osf Geophys c al.Psarc v . '73 no. '8, p., 2_569-2577.. Br uun, P.. , 1 963, I.c:'ngshore c:ur ren-ts and 1i. ngshorce -tro ug~his Journa l offGr.c:'PhYs I caI. R-eseairch . v~ 68,l Ino, 4, P , 1 065.-- Br- uj un 1-1P 195 CAs ero i on a n ci t hI e ie v e I. o p mIenrt a f b e a : hi p-ir cf i . e-s : U , S'.. Ar my , .ea c h E~rosiFon Boa rd , TechninIc alI Fi'Almor andium No. 44, 49 B~r utin, P. , a ridJ G unbak1 , AR ,1 977, St ab-. i L i ty of s, 1. op--e str c tuIIr es i n r e LatI.i o-n t o t a (/ r ri Sk c r i tr i a in d i e i.:J n cs C:a s -I a L En r, g i n r mi i, v. , p. :37--321 2. BB ti hr 1- as en J e, a nd 'Sv e-n di s en , I. i 97 9 , R e Atu l. ar woa ve(:s ri sh o:a 1. i nu wa t er- Ser i eA-. Pa per o 21 rstitueof d r d vnia f i c s a nd HIy d ra u L i c Eng ne er i nq , Tec~hn i ca L Un i vers i ty onf :D e n ~-a r k, B -r n e , R J .,-196 9, F ic L .d o c c IIr r en c s o f i nd IIc ed fu IIt i p LIc grav ItyV waves: JouIIrnrfa I. of GeonP h ys i c a I. FZ es e.a r ch , v .74 , n o 1 I0, p 2590-2596 Ca mnf i e LIcd , F .E.L , 1 980 , 'Ts unamu I e-ng i neer I ng U . 9 Army, Coasta L E:ng I neer i ny eeac Ce:nter , Spec i a I. Repor t No. 6, 222 p Ca--r ter. R . Wl. G., , and] :a Ls i 1. L ie, J.~ H.. 1 9,133 A note o:n the a (oC) u n t o f wIa v e en e-r g ' 1 a n s foi t t edci ov er n e ar s h ore san -1d ba rs : I a r 1h SuIIr f ac(:e Pr o c c. s s ( -andL L~and f ormrjs , v . 8 n o .3, P.~ 213-22 Ch a nd cl1 -r .. F. L . , a nd 'so re(-n s e n, R' . M. , 9 972, T'ran S foar fita t i onris o f waves passing a Sub merge b c a r: (- ceelinisof the. i3th CoastaLI Enciii nerinlCneecChap . 1 9, p. 35-0 Dean, R., C;., 1977, JEiu F.i ibr ium 1-:'eiich prof I Les : U. Pi t L a nt ic ~and GuLf of Mex ico coasts: O~cean Eng ineer ing Report No. -12 , Dep a rtmfenft c*f~ C ~ivl. .ni neer ing , Un iver s ity of DeLaware, Newark. Dean, W. R., j94l5, 0-n- Some cases of -the reflect ion rof Sur face waves b.-y an i nc Ji. i ed: p 1 n-e barr Ier : Cr e a t 13r i *t a i n Mi mistry of Supp Ly, Wave Report 13. De *t 1 e -1, H FL., 1 980, MiIg r a*t ion of Long sh ore bars : `r o c Peed i nnc (3S o f -the -17 th Co as ta L E nq i n ee*..r i n Co nf e r enr c ha p. 9 , P , 1 4 7e,.'i--1 4 9 2 Di ephu is, J. G. I--. F:., 1957, ScaaIc effects I nvo I.v ing the brealk-- ing of waves : Proceed i nici of -' . ~tj Con-if erence on Coasta I. Eng i neer i nq , chap . 11 , P . 1 94-201. Evan, C]. F . , 1 9 40, Trh e J. o w a nd( ba L I.of t-h !e ea ste rn sh1o r e o f Lake Michigan: Journa I of Geo Logy, v. .43, p. 4 176---SI 1 Ga i L Lardl, D., D. , 190 4 , Wla ve a ct i on i n r (-el.a ti on *t o e n gi ne e rin g st.truc tures: Proaf es s i na -,ia . P aPe r s o f t he(:0( Cr ps o f E n i ne e rs No. 31i, p . i 10-- 1 23., Gaa Lv i n.. C_ J. Jr, 1 970, F in i te---amr) I. i tukcle sha lLow wat-er waves of per ic i c a I.LIy r ec urr ing form P'r oc e (,d4 I- qc s f the., 9--mpos ittu onl Lonri Waves U n i v/e r s i' ty aof Dc e . a ware N ew a r k p. -32 C a 1.vi1 n , C. J.. , Jr i 19 69, re a leer -t r a veL a nd (--IIo i ce o:)f cl (-isi rn et h e i I- l't J cru r na I. o f t he( Wa te rw a ys andA H a rt o r i D lv - I ('31 (~~~~S me ~c . C, i v i 1. 1:q , no j I-1C W 42 , r i: Pa p. er 6569 Ha Ll. tsL C., 15931?, Pi modeL s.t ucy of -the.- ef-fec:t of subme(-rgcfe brea kwa-ter on wave act ionl . . ",' P ~r my a ceach Er- -os, i o n Bc)a rdc T c: tIIn i c a L. M e aT ra nd u ii No . -1 Ha m ma c 1, , J L , anrid 'e q u r , H ~ , -1 T97 4 Th e 1< or A64tj ewei- d e Vr i ? es eq.:;ua t- ioc)n an-Id wta t er w a ves p pa rt 2 , c o ftp ar I s onr w i thI e xp er fi E.,n ts: J ou rna 1. o f F 1. ui M e h ani cs v .. 6,5 , p t 2, p. 281:-314.. Hands, E ., B , -1976, Obse~.rvat ions o'f barried coasta 1. prof i ILes u n der *t IIe i -n f I. u -e n c e ot f r- i s i -n ~ w ate1r 1. eveN c.:Ls- , e as~t e rn L~a 1, e M i ch II ja n , -196 7 -1 9 '? U . 9 A r tY C oa st-a L E n i -n *eer i n R -?Esea-r-ch - Cen.. Y1te(:r T ec: h~ n i c: a I. Rp o:)r t Noc 76 I H a -ritna c k , 14 i 5192 4 U b e r s a cr, d-i f f e : Jahr esber. Geocv. fas He irns , , 1:. 49'50, W~ater waves over a cha nne l of -f irniite depth w it h a ~s-ub1:foer rje pc .a nebr ie C.a na d ian Jour n a I. o-f Mathematics, v.2, p. 21 0-222. Her bi c h , J . B., 9'70 , Cmoip arwi son of od .a nd b eachsou pat tem-s : Proceed i nc-I of t~a .2 Confrere-n-ce Oil Coastal. Enci iner mc:,chap, 3.0, p . i 281 --1 300. H-ow iI<awa , K<a-,-and Kuo, C.. T., , '1i966 , Af stud y onl wa ve *t r a nsm F s, o n i n s i ci e s- urT f z onre : " Coa st a I.1. En1cji -r- ne. er nc 4: vi -JJ a F)ian , I--lo)r i P a wa , K< a -i'id W i eq. 1 . ,R .L. I '-"1 959, S e oi dc aw ry w a-ve(: c:- e st s R eP o r t Sew i e s 39 Ifss ue 4 T Inst i t u t e o: f Enrs; i -n ee r i Re(--s-e a rch , [Jin i v ers i ty o f C a L.i fow)r n i a a *t 14cer Ic Le 1. e J..jhe t g I , an Ci u , 'T' . Y.. 1 19 7F3, ThIIe v ar i a t iov)ns i n be(,a chI p roc f i es w h en a pp ro)x i moa td Iny the th e o ret i c:a 1. cu kr ve: T ec:hIIn i c- a I. R e P :r t N ~o. 039, DepF)a r tent -,-1o f Co a st a I. a ndc 0 c e a -, m r a phI i c- E n g i nIeew Y i nc ,g U n i v ers t y ' of o I~r Ica C.,a: c i -v I. e. ,J ef f r eys , H..I - 194 4, Noat e oDn t he aof f shoc r e b a Pr po b I. emfi an11d -re f L c-- T i on r -fr omf a,.. bar :- 7, r eat B r i t i anr M ir n r- -t r of c upp): I. y a Wve R'eport No.. 3. Johon, F , -r14943, Waves i n -the pr"esence of ani inc Li ned biarr i ci Ccim nI : at o is In Ap p .iecc Ma'thiema*t i c-s-, v., 1 , p, 1194--200~ Jo)II ns E ).f, J . W . FuchIIs. R. A. a-ndc M ow i s on , J .R' i 9 15 1 h he d ap fi P n - a C:t i aon o sub I1. m (.? Y cd b r ca le wja t ci's- T Tr a nsact i on it e r i c: a in Geo P II s i c a I. U n i on Y-i , no . , ic 5 , P . 7 O4*** 11 3 5 1(..ady, D). if.. a-d CoLemnan, J. L., Jr., 1980, li-nc idenc~e., brea .k ing , anid r e-for ni ng cof walves, b -eh ind Subamierci ed ba -I- -I-1(.,r - Pr-o c c.. cdi I- ng s o f a.jN Sm p o)s uII c)V m, on ah ore (. t-I n es Pa s. dF______VI______ a I- r tmen t- o- f G.eo toc Lo a d.j F a S-id~I9t a te UnI i yr V y ty "Ta L L ah a s-i eu 2419 -2 6 7 ietuLegan, Gli H., 1 943, Mn exper imentaL -i. tudy of s-ubffar i e s-and b a I-rs U S E . A r mv , B Pa c: hi E: rI c)s i cn VI oa r di , T e. h I-m i c a L Rp o r 1 No., 3. K i s [I i , T ., a nd Sacek i i-i. , 1 1966, T he sh oa L i n b rea k i rig an-rd r unup of t he eso I t ar Y wa ve on im(p erm ica b L e -rough- s- l.op es Proceed i ngs of -the I Oth Conference onV C 1o a st a I lEng, inV e er nqiVi( chap . 21i, pi. 322--348. K "moa r p. F'.D. anVId G a u qha i, M . K i9 , A . y wave theory beae he~i gh t Predict ion: Pr o ceed( i V~I Is o f t h *.? 1 35t h :at a 1. Enc -Iqi jI n-eer I (..I Cor n f o-eren ce .ch!Ia p .2 , p 4 051-41 ES l.mb , HVI 1 9 45, Fhvdr o dyVInam i c s 16 th e d .. , Camnb r i d gea Unri i v er s I Piress 5 L C)n d C)n.i I. e hif mann V F' 4 P.F". 1 33 S4 , Da s kustemy ein9b i c.- t h inV t e ,poro tiF miner n s ZE? i t s d~c .~ G esAe 11. L f .Er dci 11 nd~e :14. 3 Ber- 1. i VI , v 1 9 p ..~ 3 1:1- Madsen, 0. ES , anVId M e i , C .C . , 1 9 691:, T he- trI-a n sf or fa t ion V of a so Litar y wave ov.,Ber an u-neveni b o t too: Journa I. of F"L.u cid Me.chan ics , v., 39, p t . 4, p . 7ED1--79.1 Mason, M.~ A., and Keu Legan, G,.~ H., , - 944, A wave-: met hod. for di e t e rm i ni I ny c e p t h s- o v er- b o t tom) d i s co ctV i ni u i t I es U . Ar m- aY , T e a c. h Eros ~ cio Vi Bo a -I- d , Tech ]nIr c a I. MIe mo or an ri ( ui No c 29 p.' Mc Co wan-VI , J 1 9 4 , On the higiyhest wave c:-,f paerfrmanen It .ypFe Ph i Iosop yi c: a . Maga zi n e, Ein: rgh v.. 3, p . 3S'1- *-5 .. McNa ir, E-. C., and Sorwenseni, F'. N. 1 970, Char-ac~ter ist icsc of wavesi b rok en by a l. ony shovre bar: Prorc ccii my of -the i li Con-ferenrce on OCoast a I nii erimi hp 26, p ., 41 5~-1343 Mich I J~ HI. , 1H393, On the h i hest waves i n w)ater- Phil[osrophitial. Magiazine, 5th ser ies, v. 36, p~ -4 3 --4 3 7 M i I L erI , R .~ I...., 1 9'76 , Lo ie o f voctr t i c- e s i n s urvf zon Ie p r e d i c t i o)n sed i moe nt a A i on V a nd Loa ve -f or-c es ]:n)- :e a c: h anVId Near- s hc'r e d ei fi mena t1Fs1 i o n , 9oc: i (.tv o )f I::'a I. ano c- . og idt: c M inrer--a L og i. ;Ist s ,pe c i ai. Pub1)L i c at--ion VI N )2 p., 9 2 11I.. M I I. . er - , IR I... , e t a 1 . i 9 7.4a , F i e 1. di m ea s, Ur T' i.. (-nts o)f. i mIp a C t p re ss~'UrY'e.1 n ' s-u -. Pr o c: eed j I g s of t iei c . t 11 Coat aL Viq ; i nee r iI- I,", Cc: I- fer VI e , chap .f 103f, 7, 7 1 .i --- -1 52 ~ NIL 1. e - r , L .~ , e t a I. . I 1:114 b "F Th e f -f ec: I o f b rI e a k 1I< ci, sh ape onsI- impaci pre!:-sures in1 Tucf ech-n ic~a L Report No.. 14, F .uidDyn amni c: s anid Sed iti-me.n *tranpo Laboraor D0e pa rtimeL-,nt o:)f Gcop h ys i c: a 1. ,,,c: i cenT1c e s ,Un-- i v e T. i t Y o.)f Cl I.- c . a go No i sonr, J~ R.., i949 , Model Lst*udiy ofwave. a':t imon o~n Iunde r wta te b ar r i e r s -. Report No. 1-E:1i 6-3,D4, FLu ic d Nec .-han ~c:s Labhorat ory, Dep a v.t meyt Of F'1g-ni I 1crI qig, Ivr of Cla L i f orn ri a a t '.Cqe r ke l.et:~y , 2 6 I: NuIInkli 14, H. 94 9. The-O s o 1. i Itar-y v wa ve theor-? a - y a-n d its 1 a pp 1. i c:a t ioc) n t o su ir f p r oht. I. e fs A Anni-ia 1.s c) I t h e~ N! n Ym c) A c ad em y o f c: i e n v. , 5 - N a ka murIIa, M. Eh i Y i a sh i , -I" anrid S'a sak i Y i 9,-66a , Wave ci ec a y i ng clduIe t o bhrea:m 1 ii I ng Pr oc) : e -?d i n-g s oi f t h~ 1 01 Ccj n f e e n c: e an. C oa.,s 1: a 1. E n.ci i ne er i In c , c ha p . -1 6 , p 21 3 -'2 N a k am(Iu ra N. "3 I i r i ash i H~ aIn d Sask i Y. , 9 6 6b , Wla ve(- c:lamjp i -n g e f -f c: t aof s u bmf-,ergie(Jd ci k e : Pror)c ee d i ngI (is f th IIe 01.1t C oin -f er enrfc e onTI.( coa t a- 1 EIn ci i nee I- ni r(. ch-Iap 1..~ p ., 754 -2 .7, 0 t tos, 'T' , -1 91 , Den d a -s s un-id z i -n gs t J Ja h I-bsher . C.,r ci r I'. r e is wa 1. d ,v 1 3 , p.. 339 3- 4 )3 P'utnvam I J , A., , 1 9 45, Pr e L.i (r i Ina r e por t (Jf mo d el. stuIId i es onI- thI-Ie t1r anrs iti i on c:1 f w a ves i In s h a 1. Lc i. o I water . : Rep o r t No . H1E -- I -16 --i1 06, C o 1. 1. cie o , tf EnI- 9 Ti n7? I i n U Lin i v e rs i -t Y( of Ca i. i for v-n- i a a t Ele r I., e I. e y a awa ra g i 'T aF . and I wja t a (,. *. 1 97 4 O On wa ve deI for m a I I conf a f t enI. Ifh)r e , a .1< I g F: P' oc: e ci i Ing s o) If *1 he I A1 4t Coas a L. Enii i ne er iIn ri Con IIfec.-r en vicp ch na p ..2 7 ,p I.3 4 9 1 Scot.1 TF 1 9 45 'S a n.Id mol)v e m e~nt b Y wa ves U. 'S'., Ar my, EBea ch Ercos;c B nIoa rd, 'rcch n ica 1. Nem or an ci um No 4(3 Sh epa ci , F P., 1 950 e, L.c. og shore Lrarsand h. og s-hore c t r o u gis: U. 'S' Ar my, Eie a.c:h E-ros i on Boardci Tcchfn i c a LMNemor anciu m K., Ei aet I , a . t. A. an 4 a-rid Wicl H-. (L.., -1930, 'BreakInig waves: Rep or I Mi3 7 1 Tc Te ge(,?p ast Onid e r-- o k 1, ,Ia t1 .. erst a a t 1) c 1. ft dyi L i Li as Lb oa to)r Y., i ,e !I P .. (- 5.no .... , S. . J a r. ad 1 h, i t ford ',P. .. , 6 96 , *The b- eli, a v i o)r o f s o L. i t a ry wja ves on:Iv a s t e p p dc s 1. o pe : Te chn vi c:a 1. RPep or I-t No . 3, D e p a r tiien tr o sf C' I iv i L. Eng- I g n e e v.rg Y S. FanYI f o rdc U i- i ve(.?rs5 i *t. i::a Loc AL to, c C a L. i f c)I-n i a. .St IIc: It'y, Y. a n.]ci 'Bonn.1I.[a r cd , :D .. 1: 937 , Cc:'in IF I-- b ut i o n t o tI- ie e xp erimenta, sta1. udy Yo-f fnar Inc r rackle f i L L. dii k es : r Bu I. LetI iIn Tec h_ n- Y i q: uc ci d L a . II I s se !:,' omta nci de. 53 ' F t u c k -y , A . a *,- and Bo IInIa r- cl , D0 i 9 93 8, Co ti -I r- i b ut i on-I1. -to I te oxp er i f men-Ita . 1 It ucly of r - nr I -IIe roc)c: 1, f i L I. cl i kes .' 3u I. L e t i n S uh a .. ~~~d., and Pc 'S Rcit-fandts OuaYda a I. Nad Rotrt., 1-l I.. i9T7, fWa e c: t ionr arnid s- ed iII me nI t 1: r a ns1: orIDc - to of -fr i r, iI ny c orT a 1.Y.ree.,fs: Prf oc e ec d I ncl s Tb d 1l nI t e rn a A i ona 1. CoralI l'e v m ~ os; i ur ff P o A,-en- t i e I. hi c n41o I oj - M ar i ne VIan)d A- -t m os Ih e r t c- i enc (- e , U.Jn i -ver v .,, it yv of Ma m, F1. o r idla , p6 5---7 0 'S'u th erTI LanId, A. 1.,E[- ha r-ma , J. H ,- ad S"h e Id i n , C). H.., - 97 6 W4a ve r unII- up on-I a s i mu l.an t ed b e ac: hI Fr oc e ecd i ny gs cof th In ei15 I C onIIfe!r enIc: e an I Co(saS st-a I En II 9 n eer iIIn Ur se L . , F' 1947 , ThIne e Fffe-Ac t o) f a -f i x ecl v e rt i c a .I-. Ia rr i erI o n u Ir *f a c:e(- w a ves iv n dee p w a t er- P r oc: - e (-?d II nqsj o f the C a mb r-)I i d -I e Ph i. r. o Po h i r:a 1. oc: i et v N./ 43 p 374-382. U. 'S Arm y . I5 97 7 , "?Incor e F, rocjt ec 1t io MT.LI. U.'I S (. y , C c: as.ta 1. E-ny gi-I neer -- I nyF es ea r- c: hI- Cete 3 VI. s. V a n 1) :oo-I I , , .G. , 9 I "73 8, B r ea le i ny I f na r i ants1 i nI s h co a- Li. I- ny wa;4v : Jo',.ntI- a 1. co f Ceoa phv %,i ca 1. lRe search v ..8 33, ino CI C6 W e i shIIar-- l.- L ., , an--)d B yrri-Ie , R. J , 1979, F ic e Id s t u dy o) f b re a k i ncis wave cna-rac teri 1stji cs FrToceecl irnys of the 1 6t1h "rt erina t iona I. Coinfere--nc~e on CoastalI.7 Enyignee-r-I nci cheap. 27, W oocdc , W . L.i - 1 97 0, Trr anI- s f o rm a t i( I os o f hrI- ea-. 1 i nci w ,, a ve. ch;Ia r a c:: t erI. I st,.k j c::.: s ov er a s, itb mar I- n Ie b)a r : Te c: II nI ic: a I. RepI o r -t N o .. 4 , D e pa r- t mriein t o f Na i: t urI- a S.Ec- i en, Ic: e , M i ch- In yan--I Sa te IU II i rs i t y , s -IEa s , st a ns ny , -1 1 ' p. Woc)od , [,I L. . , 1 97 1 , Tr a rinsfor ma t1 i I on of bhr e a k1< -ig wave p a ramete r s over as A, bmar iI ne bar PhI .0 1). .D i s er tat i onT )C-, I ea r tmIIenI- t. of Cye o 1.o(-)q y M i ch In ya n S tate(:?L iniv e rsi t y, E a st L-.ains.1) Z a bu sk y N. J. anIId G a L vi II, C. J, J r. I 9 71 , Sh na LI. clow-Iwate r wa ves, th]Ie K or t eweg -cleVr i e s eq. ua t i on a ncl s o L i tonsY- Jourinal. of FlEuid Mechainic:s, 1 V. 7 p t. 4 , p.3 1-02.4. 54