A Generalized Nonlinear Model for the Evolution of Low Frequency Freak Waves

摘要: This paper presents a generalized model for simulating wavefields associated with the sea surface. includes case when ‘freak waves’ may occur through an effect compounded in nonlinear (cubic) Schrodinger equation. After providing brief introductions to linear wave models, and equations, we present unified that provides piecewise continuous transition from state. is based on introducing fractional time derivative develop partial differential equation stochastic source function. In order explore characteristics of this equation, consider separation variables approach derive governing equations spatial temporal behaviour. Models function (which, physical terms, describes conversion wind energy into energy) are also considered separable basis. With regard characteristics, provide new assuming Levy processes time-dependent velocity informed by experimental data. We frequency generalization Berman Ornstein-Uhlenbeck processes. statistically self-affine which has synergy Pierson-Moskowitz spectral form fully developed driven seas ‘similarity theory’. Having presented solutions explored using Green’s transformation under low bandwidth condition. Iterative methods solution then threedimensions two-dimensions. Example results considering first equivalent application Born approximation The simulations evidence formation freak waves being related fact force (as time) non-Gaussian ∗Dublin Institute Technology, Kevin Street, Dublin 8, Ireland; http://eleceng.dit.ie/blackledge; jonathan.blackledge@dit.ie; +35 31 402 4707. distributed. Consequently, more common than would be expected Gaussian statistics.