Simulation of Nonlinear Spatial ‎Internal Waves in Seas and Oceans with Density Jump and Gently Sloping ‎Bottom

Arkhipov D.G., Safarova N.S., Khabakhpashev G.A.

The combined approach is proposed for the transformation description of the pycnocline three-‎dimensional perturbations over a fixed rigid bottom in the “solid lid” approximation. It is presumed that ‎wave lengths are moderately large, wave amplitudes are small but finite, and the bottom may be weakly ‎sloping. The deduced system of equations may be applied for a simulation of disturbances propagating ‎simultaneously in arbitrary horizontal directions. The basic nonlinear equation for perturbations was cal-‎culated using implicit finite-difference scheme, and the linear auxiliary equations for the velocity field ‎determination are solved by the method of fast Fourier transformation. The used algorithm was tested ‎with the help of the plane waves dynamics problem. The solutions of several characteristic planar ‎problems were found numerically, and the effect of the bottom topography on the evolution of ‎disturbances which are lengthy or solitary in space was shown.‎

Download original text