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A numerical study of three-dimensional orographic gravity-wave breaking observed in a hydraulic tank

Numerical simulations with a non-hydrostatic anelastic model are carried out to reproduce hydraulic tank experiments on stratified flow past a two-dimensional mountain ridge, for a Froude number of 0.6 and a Reynolds number of 200. The gravity wave thus generated steepens, overturns and breaks. Numerical simulations and experiments are directly compared showing close agreement. Ground friction is found to have a major influence. It induces a boundary-layer separation on the lee slope of the mountain and a low-level trapped lee wave inhibiting the downstream propagation of the breaking region above. Consequently, the three-dimensional vortices generated within the unstable two-dimensional overturning wave have a toroidal shape in agreement with experimental observations. Sensitivity to the shape of the initial three-dimensional perturbation is studied. In the case of harmonic disturbances, spectral analysis reveals that during the growth phase of the instability, harmonics are coherently produced by the nonlinear transverse advection term. During the later phase of quasi-steady turbulence, the vortices have a morphology that does not depend on the type of the initial perturbation.