Transformation of Nonlinear Surface Gravity Waves under Shallow-Water Conditions

Nonlinear edge waves and shallow-water theory

Patterns and statistics of in-water polarization under conditions of linear and nonlinear ocean surface waves

[1] We study the polarization properties of the light field under a dynamic ocean surface using realistic linear and nonlinear ocean surface waves. The three-dimensional polarized radiative transfer of the dynamic ocean–atmosphere system is considered using a Monte Carlo vector radiative transfer simulation for arbitrary depth. The program is validated with measurement data taken in Hawaii duri...

NOTES AND CORRESPONDENCE A Shallow-Water Model that Prevents Nonlinear Steepening of Gravity Waves

The shallow-water model is used as a testbench for understanding many fundamental dynamical problems (e.g. certain wave–mean interaction problems). One sometimes wants to allow large-amplitude gravity waves to propagate significant distances in such models without forming shocks. This paper presents a simple, and apparently unique, modification of the standard shallow-water model that prevents ...

Nonlinear refraction-diffraction of waves in shallow water

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K-P equation (Kadomtsev & Petviashvili 1970) to incl...

Interaction of surface waves with vorticity in shallow water.

Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well as the scattering of surface waves by vorticity. In a first Born approximation the radiated surface elevation is linearly related to the Fourier transform of ...