Oscillating wind with a period P induce variability with the following characteristics in the upper few hundred meters of the equatorial zone (5øN to 5øS) of the ocean. (1) P < 10 days: these winds fluctuate too rapidly to generate strong currents and excite primarily waves. (2) 10 days < P < 50 days: At these periods the winds generate intense equatorial jets in the upper 50 m, but at greater ...

This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentumconserved advection scheme enables modeling of breaking waves without the aid of ...

An algorithm for the solution of general isotropic nonlinear wave equations is presented. The algorithm is based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral space. The remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure. Solving the linear part of the...

The nonlinear self-interaction of an electrostatic surface wave on a semibounded quantum plasma with relativistic degeneracy is investigated by using quantum hydrodynamic (QHD) model and the Poisson’s equation with appropriate boundary conditions. It is shown that a part of the second harmonic generated through self-interaction does not have a true surface wave character but propagates obliquel...

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude ...

Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present bo...

We study the spatial and temporal structure of nonlinear states formed by parametrically excited waves on a fluid surface (Faraday instability), in a highly dissipative regime. Short-time dynamics reveal that 3-wave interactions between different spatial modes are only observed when the modes' peak values occur simultaneously. The temporal structure of each mode is functionally described by the...

We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of dissipation and of material and geometric stability. In particular, the analysis provides bounds on the constitutive parameters and on the predeformation that ensure linearized stab...

Generalized solitary waves arise in many physical systems, including water waves with surface tension and multi-layered fluids [7,19,21,22]. They are nonlinear long waves consisting of a localized central core and periodic non-decaying oscillations extending to infinity. They arise whenever there is a resonance between a linear long wave speed of one wave mode in the system and a wave speed wit...