Download e-book for iPad: Advances in Coastal and Ocean Engineering by Philip L. F. Liu

By Philip L. F. Liu

ISBN-10: 981024620X

ISBN-13: 9789810246204

ISBN-10: 9812794573

ISBN-13: 9789812794574

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164) To return to physical space, we use operator correspondence where we have to account for the fact that K is the change of wave number relative to fco. Writing K = (KJ, K2)T, we thus have, > idx fco fco and > idv . (165) In physical space, we then have, dA — +L(dx,dy)A = 0, (166a) with L(dx,dy) = »{[(1 - idx)2 - d2v}l,i - 1} , (166b) and thus, —- + —~ dKi{uj{k0 + K) - tuo] / dx'eiK

18 M. W. Dingemans SI [{- & A. K. Otta dB 2 dA + Mi drj 4 , aX2 fd(f> (xD3 (d± d£ drj d^drj. (59d) These conservation laws can be useful as a check on numerical computations of NLS-type equations. 3 . 5 . Special cases of NLS-type equations In the reduction to the I D case, the dependence on the lateral coordinate 77 is ignored. 0) dt where the condition d^1^ /d£ given by: «2 v\ = Xi -X2 • (60c) T h e long-wave potential (T>(1,0) can be determined after the complex amplitude has been determined from the NLS equation (60a).

172) reduces to: — + cg • VB = -i fff dfeidfeadfcaC^a , (175) which is called the inhomogeneous Zakharov equation by Rasmussen. By considering a Stokes wave with constant amplitude, B{k,t) = BeiatS(k~k'), (176) 52 M. W. Dingemans & A. K. Otta Rasmussen poses the question how much k' may deviate from its exact value without changing the n a t u r e of the solution. P u t in another form: what is the appropriate value of the bandwidth for application to r a n d o m waves. To this end, the solution is multiplied by a small variation due to a small p e r t u r b a t i o n wave number K, B(k,t) = Be

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Advances in Coastal and Ocean Engineering by Philip L. F. Liu

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