| This paper deals first with the mathematical formulation of a non-linear second-order stochastic model of free irrotational ocean surface wave on deep water. Then, the case of wave motion of zero bandwidth is treated to illustrate the model. On the basis of the usual hydrodynamic equations, the formulation is made by successive applications of the harmonic decomposition and the so-called Wiener-Hermite functional series expansion of random functions. This procedure yields the kernels equations. These kernels allow to obtain the random surface wave fields from the Wiener set of elementary random processes. For the particular case cited above, as expected, the second-order non-linearity results in the generation of a second harmonic component of the... |
