A NUMERICAL SOLUTION FOR THE COEXISTING FIELD OF SURFACE AND INTERNAL SOLITARY WAVES

Abstract

 The numerical solutions, for the coexisting fields of surface and internal solitary waves, were obtained using the nonlinear wave equations, based on the variational principle. In the coexisting fields of the surface and internal solitary waves, the phase velocity of the surface-mode solitary wave, was smaller than that of the surface solitary wave for the corresponding one-layer fluid; conversely, the phase velocity of the internal-mode solitary wave, was smaller than that of the corresponding internal solitary wave without a surface wave. The maximum wave height of the internal-mode internal solitary wave, was larger than that of the corresponding internal solitary wave without a surface wave. The wave height ratio between the internal-mode surface and internal solitary waves, was smaller than the linear shallow water solution; their difference increased as the relative wave height of the internal-mode internal solitary wave increased.