Two‐dimensional instability of finite amplitude internal gravity wave packets near a critical level

Abstract

A high‐resolution two‐dimensional numerical model is used to simulate the propagation of finite amplitude internal wave packets into a mean shear flow that varies slowly in space. For moderate packet amplitudes the interaction is well described by weakly nonlinear asymptotic theory. At higher amplitude, however, a region develops near the critical level in which nonlinearity dominates, the wave packet becomes unstable, and the wavelike motion breaks down into smaller scales. The form of the observed internal wave breakdown is unexpected in that convectively unstable density gradients persist for many buoyancy periods. The eventual rapid transition, from large‐amplitude wavelike motion to a more complicated flow, is triggered by an instability driven by the intensified wave shear and not by a convective breakdown of the unstable stratification. This illustrates that unstable stratification does not necessarily lead to convective instability in two dimensions.