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Three-dimensional wave instability near a critical level. (English) Zbl 0846.76030

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. The authors use a three-dimensional numerical model to study the behaviour of internal waves at critical levels. There are two motivations to investigate the three-dimensional aspects of this problem. The first is to check the prediction of linear stability theory, namely that instability should develop through convective rolls oriented spanwise to the ambient shear. The second is to quantify the distribution of energy between various components of the flow fields, i.e. the incident wave packet, the mean flow, reflected waves, mixing and dissipation. Three-dimensionality develops by transverse convective instability of the two-dimensional wave, and the initially two-dimensional flow eventually collapses into quasihorizontal vortical structures. A detailed energy balance is presented in the latter case.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76D33 Waves for incompressible viscous fluids
76V05 Reaction effects in flows
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