Chap 2. Statistical Properties and Spectra of Sea Waves

Transcription

1 Cha. Statitical Proertie ad Sectra o Sea Wave. Radom Wave Proile ad Deiitio o Rereetative wave.. Satial Surace Form o Sea Wave Log-creted wave: Wave cret have a log etet well, eecially i hallow water Short-creted wave: Wave cret do ot have a log etet, but itead coit o hort egmet wid wave i dee water.. Deiitio o Rereetative Wave Parameter I ature, o iuoidal wave eit Wave orm are irregular or radom Diicult to deie idividual wave Zero-croig method i ued.

2 Aume that we meaured t at a oit. Zero-ucroig: Zero-dowcroig: Statitically, zero-ucroig ad zero-dowcroig are equivalet i the wave record i log eough. But zero-ucroig i more commoly ued.

3 Arrage the wave height i decedig order. a ighet wave:, ote: i ot the imum wave eriod i the record, but the wave eriod correodig to. b ighet oe-teth wave: /, / Average o the highet / wave / / / i i / = average o the wave eriod correodig to the highet / wave c Sigiicat wave, or highet oe-third wave: / 3, / 3 or, / 3 / 3 i / 3 i d Mea wave: or, i i

4 . Ditributio o Idividual Wave eight ad Period.. Wave eight Ditributio Gauia tochatic liear theory or arrow-bad ectra rage o eriod i mall ugget Rayleigh ditributio o dicrete = cotiuou or large. i Probability deity uctio: e 4 with atiyig d Probability o eceedace: P e d e 4 4 ~ robability arbitrary ~ give Field data idicate that Rayleigh ditributio baed o retricted aumtio liear + arrow-bad yield good agreemet with data.

5 .. Relatio betwee Rereetative Wave eight Eceedace robability baed o Rayleigh ditributio P 4 e / l or give e.g., = 3, By deiitio d d d / / / Uig d dp ad d P 4 e d Pd P d P P d d dp / 4 e 4 e ] [ uig comlemetary error uctio, t dt e erc, dt t / e 4 e erc / with / l

6 See able. 373 or / / v,5,,, / 3. 6, /. 7, / Ditributio o Wave Period ot well etablihed. Local wid wave ~ + Swell ~5 two eak bi-modal or two mai directio yically,. ~.3 / / 3.3 Sectra o Sea Wave.3. Frequecy Sectra Free urace ocillatio at a oit: t a co t where a = amlitude o wave with requecy = hae o wave with requecy

7 Eergy o wave with requecy = ga Real ea wave iiite umber o requecy comoet cotiuou requecy ectrum ote: a S a S

8 Stadard ectra eemble average o large umber o wave record Bretcheider-Mituyau ectrum Fully develoed wid wave i dee water eergy iut rom wid = eergy diiatio due to breakig S.57 e[.3 ]. or give ad. Modiied by Goda 988:.57.5,.3.75 a i Eq... JOSWAP JOit orth Sea WAve Project ectrum Growig wid ea i dee water S J 4 5 e[.5 4 ] e[ / ] where J J.3,.4 a b.7.9 or or eak ehacemet actor ~ 7 tyically 3.3 eed to eciy,, a, b, ad harer ectral eak a.

9 Suh et al., Coatal Egieerig 57, howed that or deewater wave aroud the Korea Peiula, the robability deity uctio o i give by a logormal ditributio: e.53 l with it mea equal to.4, which i omewhat maller tha 3.3 i the orth Sea. 6 itogram Logormal PDFm=.63, = umber o g 8.4 Probability Deity g

10 3 MA ectrum Bouw et al., 985, J. Geohy. Re., 9, C Iclude eect o iite water deth S MA S, h J k Kitaigordkii hae uctio deth eect.5 h k, h.5 h or or or h h h h h / g /

11 .3. Directioal Wave Sectra Geeral requecy ectrum aume wave with may dieret requecie but igle directio. owever, real ea wave coit o may comoet wave with dieret requecy ad dieret directio. hereore, we eed directioal wave ectrum: S, S G directioal readig uctio directioal ditributio o wave eergy varie with requecy. G d rereet relative magitude o directioal readig o wave eergy otal eergy = S, dd = S G dd = S d

12 Mitutau-tye directioal readig uctio Baed o ield meauremet, G G co ymmetric about = wave agle rom ricial directio See Fig.. or the variatio o G veru. Ituitively, G or 8 9 ad 9 8. But, G i very mall a log a i large. Mut atiy co G d Symmetric about : G co d G co d [ ] where Gamma uctio! or iteger.

13 deed o requecy : / / 5.5 or or where = eak requecy, ad roughly. 5. at, ad decreae a icreae. ece, directioal readig i the arrowet ear. See Fig.. or where * / = at eak requecy. 3 Etimatio o the readig arameter A icreae, more log-creted. etatively, or wid wave 5 ~ 75 or well i dee water. icreae a / L decreae ee Fig..3. owever, Suh et al., Coatal Egieerig 57, howed that or wid wave o.3 / L.55, the mea value o meaured i omewhat greater tha that i Fig..3.

14 5 Sreadig Parameter, S /L hey alo howed that the robability deity uctio o uctio: i give by a logormal.6 e l itogram Logormal PDFm=3.3, =.6. 8 umber o 4.8 Probability Deity

15 A wave roagate to hallow water, they become log-creted due to reractio. I other word, icreae a h decreae. O the other had, icreae more raidly with decreaig h or a larger icidet agle becaue o more reractio ee Fig Cumulative ditributio curve o wave eergy Read tet. 5 Other directioal readig uctio Simlet:!! l l co or l!! G G or.3 which i ideedet o. SWOP Stereo Wave Obervatio Project: G G ;.3 Eq..3 with l ad.3 are imilar to Mituyau-tye with, though the eergy read with i ot the ame. Wraed ormal uctio Borgma, 984: G e co = mea wave directio = directioal readig arameter broad directioal readig a

16 .4 Relatiohi betwee Wave Sectra ad Characteritic Wave Dimeio Wave - by - wave aalyi time domai Wave ectrum requecy domai relate each other. t a co t a co t a co t dt Uig orthogoality, co m t co t dt i m, a S d a co t dt m where m = zeroth momet o S = variace o t Deiig rm = root-mea-quared value o t, we get rm m For Rayleigh ditributio o,

17 4 4 m rm Sice ad 4 m are ot eactly the ame, ue / 3 = average height o highet /3 wave rom zero-croig method m 4 m = ectral etimate o igiicat wave height A or wave eriod,. 95 m / m ; m S d = d momet o S