Three-dimensional wave instability near a critical level

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Abstract
The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.