Theoretical and experimental investigation on strongly nonlinear internal solitary waves moving over slope-shelf topography

摘要

The variable-coefficient modified Gardner equation is proposed to describe large amplitude internal solitary waves (ISWs) propagating over slope-shelf topography. The model is adapted from weakly nonlinear Gardner equation by adjusting its original coefficients such that the model is capable of representing the crucial characteristics of large amplitude ISWs, including the effective wavelength and wave speed. To numerically solve the nonlinear equation, the fourth-order Runge-Kutta method is applied for temporal discretization, second-order central finite difference numerical scheme is implemented for the space discretization and the iterative scheme is applied to treat the coupling term of time and space. The numerical method is then verified by comparing fairly with laboratory experiments. It's found the variable-coefficient modified Gardner model is a reliable theoretical tool to describe the behavior of large amplitude internal solitary waves passing through bottom topography.