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.