Nonlinear Internal Solitary Wave on a Pycnocline

Abstract

This paper describes the theory of nonlinear internal-solitary waves of the type observed in coastal seas. It also describes a numerical solution of an initial-value problem that leads to an internal solitary-like wave. The equations solved numerically are the Navier-Stokes, diffusion, and continuity equations. The computer solution illustrates that solitary-like waves are easily generated. A comparison with the theory illustrates that the wave is a KdV-like solitary wave. Hence, the computed wave is caused by a near balance between dispersive and nonlinear effects. However, the shape of the fully-nonlinear solitary wave is fore-aft asymmetric with a relatively long, somewhat elevated tail. This feature is characteristic of the computationally derived wave as compared with the fore-aft symmetry of the theoretical wave. (This work is motivated by the fact that internal solitary-like waves have practical importance in the design of offshore structures and on the acoustic properties of the sea, among other environmental consequences.)