NONLINEAR-THEORY OF INTERNAL WAVE-TRAPPING IN A HORIZONTALLY INHOMOGENEOUS PYCNOCLINE

The nonlinear theory of short internal wave (IW) propagation in a horizontally inhomogeneous pycnocline is presented. The analysis of IW evolution near the trapping point, where the Brunt-Vaisala frequency coinsides with the IW frequency, is of particular interest. In the linear approximation the IW amplitude infinitely grows near the trapping point due to the slowing down and focussing of IW. The nonlinear generation of long low-frequency IW of higher modes by IW packet leads to stabilization and algebraic decreasing of IW packet amplitude near the trapping point. The results of numerical simulation of IW dynamics taking into account the dispersion and nonlinearity are described.