A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone

Abstract

A nonlinear model is developed, based on the rotated-modified extended Korteweg-de Vries (reKdV) equation, of the evolution of an initially sinusoidal long wave in the coastal zone, representing an internal tide, into nonlinear waves including internal solitary waves. The coefficients of the basic equation are calculated using observed conditions for the north west shelf (NWS) of Australia. The roles of both quadratic and cubic nonlinearity, the Earth's rotation, and frictional dissipation are discussed. The combined action of nonlinearity and rotation leads to a number of intersting features in the wave form including solitons of both polarities, "thick" solitons, and sharp waves with steep fronts. It is shown that rotation is important for modelling the evolution of the internal tide, even for the relatively low latitude on the NWS of 20° S. Rotation increases the phase speed of the long internal tide, reduces the number of internal solitary waves that form from a long wave, and changes the form of the waves. The effects of nonlinearity on the vertical modal structure of the internal waves are also discussed. Results of numerical simulations are compared with current and temperature observations of the internal wave field on the NWS which show many of the features produced by the generalized KdV model. Copyright 1999 by the American Geophysical Union.