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

By Philip L. F. Liu

ISBN-10: 981024620X

ISBN-13: 9789810246204

ISBN-10: 9812794573

ISBN-13: 9789812794574

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Example text

The Zakharov equation has been reconsidered by Krasitskii (1994) who showed that previously used forms did not give a truly Hamiltonian system of equations; this had to do with the definition of the interaction coefficients. It appears that in the older form of the Zakharov equation, the coefficients were not sufficiently symmetric. For an extensive discussion of these matters is referred to Krasitskii (1994) and Badulin et al. (1995). As put forward by Krasitskii (1994), the symmetry conditions are not clear without considering the Hamiltonian formulation.

1990), C(x, t; X, T) = l-A(X, T) exp[iX(x, t)] + CC , *(x,z,t;X,z,T) = - i g A £ T ) C O S ^fc; Z)] exp[ tX (x,t)] + CC, (180a) (180b) with x(x,t)= dx'k(x')-cjQt, (180c) where the carrier wave frequency u is determined by: w = u)r + k • U and J^ = gk tanh kh, (180d) and fc is given by: k = Vx{x,t).

Equation (93) with the coefficients defined by Eq. (94) e is an extension of the equation derived by Djordjevic and Redekopp (1978) and represents a general one-dimensional modulation equation for narrow-banded short waves on an ambient current or a long wave (long enough compared to the short waves to validate the scales of Eq. (92). For an opposing current, waves are prevented from propagating upstream as the group velocity cg becomes zero. The equation fails near such points and its validity is limited to milder opposing current such that the blocking condition is not met.

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


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