Interfacial non-linear waves propagating in a two layer medium are qualitatively changed due to the action of a vortex-sheet. In the frame-work of the so-called shallow water theory, linear wave speeds of the barocline modes are determined . The differential equation describing the interface elevation is derived . The coefficients of this equation are functions of the stratification, the depth ...

The purpose of this paper is to study the discontinuous solutions to a shallow water wave equation with relaxation. The typical initial value problem of discontinuous solutions is the Riemann problem. Unlike the homogeneous hyperbolic conservation laws, due to the inhomogeneity of the system studied here, the solutions of the Riemann problem do not have a self-similar structure anymore. This pr...

Dispersive effects induced by weak hydrostatic imbalance in the presence of topography and stratification are incorporated into a new model of barotropic (vertically integrated) mesoscale ocean dynamics. This barotropic model is obtained by first expanding the solutions of three dimensional Euler-Boussinesq equations in a regular perturbation expansion in terms of the several small dimensionles...

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating p...

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su-Gardner (or one-dimensional Green-Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular ...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

[1] The three-dimensional (3-D) shoaling of large-amplitude internal waves (LAIW) is studied in the framework of a fully nonlinear nonhydrostatic numerical model. The vertical fluid stratification, parameters of the propagating waves and bottom topography were taken close to those observed in the northern part of the Andaman Sea. It was found that three-dimensional evolution of LAIWs propagatin...