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The time-dependent boundary layer induced by a weakly nonlinear solitary internal wave in shallow water is examined through direct numerical simulation. Waves of depression and elevation are both considered. The mean density field corresponds to that typical of the coastal ocean and lakes where the lower fraction of the water column is subject to the stabilizing effect of a diffuse stratification. Sufficient resolution of the “inviscid” dynamics of the boundary layer is ensured through use of a Legendre spectral multidomain discretization scheme in the vertical direction. At higher Reynolds numbers, where the simulations become underresolved, because of restrictions in available computational resources, spectral accuracy and numerical stability at the scales of physical interest are preserved through use of a penalty scheme in the vertical and explicit spectral filtering. Thus, a highly accurate description of the qualitative dynamics of the wave-induced global instability is possible and finesca...

Numerical Investigation of Solitary Internal Wave-Induced Global Instability in Shallow Water Benthic Boundary Layers