Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Second Order Waves Generated by Ship Motions
Second Order Waves Generated by Ship Motions
Pages 143-156
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From page 143... ...
Pattern of the second order wave is discu -.1 in the ight of asymptotic nalysis nd a theoretical method of predicting the second order wave is te ted in its accu acy on the measured wave contou maps 1. INTRODUCTION Rational umderst riding of se keeping nd accu ate prediction of ship behaviors in rough seas are required more th n ever Non inear the ory of th ee dimensional flow of ships, moving at fo ward peed in high waves, is indi pen able for these to be feasible That is why variou non inear theories nd computational method have been proposed nd implemented However ex perimental evidence directly suppo ting or dis proving those theoretically sophisticated meth od is scarce This is what I argued at 22nd ONR Symposium as well ( Oh u u (1998)
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From page 144... ...
is the steady wave elevation the domin nt part of whi h is the Kelvin wave pattern It will cont in possibly the higher order effect resuting f om the interaction of the os illatory part The sec ond term is the oscillato y part at the f md men tal f equency nd the third is of the second har monics M in part of the f md mental f equency term will be the inear effect nd the second har monics part will be the second order effect The u teady waves might be interacted with the steady part It is however impossible to confi m it by experiment becau e the u teady waves without the te dy part is not re istic to be compared with the one with it as long as the ship has forward peed; the u teady waves gen erated by the ship motion at no forward speed is physica~ly other thing th n what we are con ce ned Con i tency nd repeatab ity of the mea su ed waves are mo t pe fect It enables u to d aw accu ate wave contou map with the resu ts of the repeated measurement The teady wave component is hard y ffected by the existence of the um teady motion; the steady f ee su face eL evation measu ed when the ship model is given oscillatory motion is in good ag eement with the one when it is towed on c m water at the s me speed with the motion uppressed One excep tion we observed so far is a sma~l te dy depres sion of the f ee su face in ve y f ont of bluff bow produced by the effect of the wave diff action S175 model was forced to pit h at two differ ent mag itudes expecting the larger non inearity with the larger mag itude of motion Ou com puterized wave measu ing y tem enables u to obt in the in t nt neou wave contou map of the fi st harmonics ~ component nd the second harmonics 2w component separately The former is con idered to corre pond to the fi t order ef fect nd the latter the second order effect x mples of the measu ed wave contou map are shown in Figs 1 nd 2 Figu e 1 is two snap shots of the contou map of the fi st order :~e2~2, the upper part of the figu e represents the real part of :~ (cos com ponent ) nd the lower part the negative of the imaginary part ( sin component )
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From page 146... ...
I-m is noticeable in Fig 1 The ine connecting the peaks of the wave system m kes about 21° with the r i xis Wave pattern of Fig 1 most perfectly ag ees with the pre dieted on inei: iviiumptioni i: i described later Figu e 2 is the napshots of the in it: nta nexus f ee su face elevation of :2ei2~2 at the so me condition of f equency of pitch i nd the ship speed, i nd with the so me no malization i: i Fig 1 While the contou map c: n be d awn with this ci: ie, we display the wave elevation on y g ada tionally; it appe ently exhibits the eke acted tics of the wave pattern more di 4inctly ~ mea su ed at h f the i mplitude, not shown here, does not reveal so clei Iy the featu e of the wave pat tern It uggests :~ will be of the second order with re pect to the i mp itude of the motion Existence of the second order waves, whose mag itude is 15 to 20 percent of the fi 4 order's, wi: i confi med. Wave pattern demon4rated in Fig 2 is so distinct that it is cert in that it hi: i a clei: physical mei: ing Two wave system; i: e seen in Fig 2 One wave is most ike the wave y 4 em seen in Fig 1; the ine connecting the pealcs of the wave system m kes about 21° with the r is, though the wave length ( the dist: nce between two adjacent pealcs )
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From page 147... ...
642 They are the s me as the ngle shown in Fig 1 nd the dist nce between two mark it confines that the wave v. hem we see in Fig 1 is the k2 wave system We Judy a wave system of the narrow am gle of 13 5° we see in Fig 2 in the ight of the inear theo y The wave y hem in Fig 2 is of the second order, yet the inear theory c n captu e one featu e of it As expl ined in the previou section, the wave field of the second order will be interpreted to be composed of the f ee wave component that satisfies the body non inear but the f ee surface inear condition nd the boumd component that sati lies the f ee su face non in ear but the body inear condition At radiation problem we may consider the former as a in ear wave with the second order body boundary condition at the f equency of 2w Natu all-.
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From page 148... ...
nd (12) are the higher order will be necessary, though it has the second order condition for ¢~ nd never been attempted Theoretical approa is we u e here for the 2 5D theo y is not a f y non inear time dom in computation but a pe tu bation nalysis up to the second order in the f equency dom in A reason is to make the second order effect more distinct; direct companson of the f 1.
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From page 149... ...
The fo mer will be the f ee wave part due to the body non inearity nd the latter the boumd part due to the f ee su face non inear ity Ou computation of both parts revealed that the wave elevation by the fo mer part is so sma~l compared with the latter's effect W ile this is true on y with the wave elevation close to the ship nd the f ee wave part due to the body non inearity is signiflc nt behind the ship model as shown in the previou section, we may ignore it in ou computation of the wave elevation rela tively close to the ship We concentrate hereafter ou computation on y on the boumd te m due to the f ee surface non ineanty When we umder st nd ;~ nd ~1~ st nd for this term, then the body condition will be O (24) The f ee su face condition (17)
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From page 150... ...
n is the so me 3 3 for the fi st order except that the sine component represent the wave elevaation at 2wt = 1r/2 It appe3 s that the genera featu e of the wave elevation is predicted by the 2 5D theo y It me. 3 that the second order wave elevation observed close to the ship might be the boumd component caused by the f ee surface non ine3 ity 3 3 sugg cited in the previous section The relatively 13 ge wave elevation of the second order is not predicted by ou theoretics method It may not be su pricing because the prediction of the fi st order wave is not so correct in the mag itude of the wave The theoretics resu t on the second order wave elevation f3 behind the ship is not av ilakle ( the 2 5D theory is not capable of computing the wave field behind the ship's Bern )
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From page 151... ...
V idation of Theoretical Method for Ship Motion by Means of Experi ment, Proc 22nd Symposium on Naval Hyd o dyn mics, Washington DC Ohku u M nd Wen G (1996) Radiation nd Diff action Waves of a Ship at Fo ward Speed, Proc 214 Symposium on Naval Hyd odynan~ ics, T ondheim Sclavoumos P (1996)
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From page 152... ...
S175 2m model 03 X/L= 04 02 00 02 04 03 oo 01 02 03 04 0 i 03 07 Y/L Fig 7 Wa:ve elevation (Ist order, Sin) S175 2m model ~, X/L=040 ( Ist sin component )
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From page 153... ...
24 3D-Computed wave pattern ( 1st oder )
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From page 154... ...
S175 2m model X/L=0 24 ( 2nd cos component <0 20 T T T T O ti = 010 = OOi = 000 O i = 010 = Oi n n n ~ S175 2m model <0 20 T T T O ti = 010 ~ ~ OOi .
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From page 155... ...
S175 2m model S175 2m model X/L=0 52 ( 2nd cos component ) X/L=0 52 ( 2nd sin component 0 20 ~T1T ~ ~ <0 20 ~r ~T _ v Amp 0 0370m F v Amp 0 0370m O t5 ~ ~ ~ Theoretica1(2 5D)
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From page 156... ...
AUTHOR'S REPLY We are too mtere bed m the second order mteraction of She ready md un decdy ship wa.es First of all w must know that the effect of the unsteady waves upon She stecdy ones will be observable but not vice verse Reason is that She unsteady wa.es not under She inf uence of She stecdy waves is not realistic for the case of our concern i e Hen c ship has forward peed While w have not deported the result here but ce tamly w mesmed the ready ship wave without the ship motion or mcident waves, md compared it with She decdy wave component of the .s.e motion when c ship is forced to oscillate or in the incident waves What w have found is chat She stecdy wave is hardly effected by the mmstelrdy wave et least for the mcgnit de of She oscillation w adopted m our mernnema~t In other words the stecdy component of the wave motion Hen She ship is oscilEdmg cg es wish She heady wave et no ship motion One exception is that She stecdy wave m fi ont of very blmmt bow is depressed slightly when She ship is m incident waves
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