Numerical Simulation of Shoaling Internal Solitary Waves in Two-layer Fluid Flow

Abstract

In this paper, we look at the propagation of internal solitary waves overthree different types of slowly varying region, i.e. a slowly increasing slope, a smoothbump and a parabolic mound in a two-layer fluid flow. The appropriate mathematicalmodel for this problem is the variable-coefficient extended Korteweg-de Vries equation.The governing equation is then solved numerically using the method of lines. Ournumerical simulations show that the internal solitary waves deforms adiabatically onthe slowly increasing slope. At the same time, a trailing shelf is generated as theinternal solitary wave propagates over the slope, which would then decompose intosecondary solitary waves or a wavetrain. On the other hand, when internal solitarywaves propagate over a smooth bump or a parabolic mound, a trailing shelf of negativepolarity would be generated as the results of the interaction of the internal solitarywave with the decreasing slope of the bump or the parabolic mound. The secondarysolitary waves is observed to be climbing the negative trailing shelf.