A weakly nonlinear evolution model for long internal waves in a large lake

Abstract

A wind-forced weakly nonlinear weakly dispersive evolution model is derived for a continuously stratified circular lake of slowly varying depth under the effect of the Earth's rotation. The model was numerically integrated to investigate the evolution of long internal waves of vertical mode one for various sets of environmental parameters. It is demonstrated that the Kelvin wave steepens as it propagates, and the steepened front subsequently generates a train of oscillatory waves. It is demonstrated that Poincaré waves do not steepen, but their amplitude is modulated in an oscillatory manner with time, exhibiting a pseudo recurrence character. The model was applied to the wind forced problem, confirming that Kelvin and Poincaré waves are the dominant response. Energy partition among Kelvin and Poincaré wave modes is estimated as a function of wind-forcing parameters. For large lakes, the most significant wave amplitude is found in the Kelvin wave mode, but the gross field energy is most significantly contained in Poincaré wave modes.