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Internal waves and boundary layers in a density-stratified fluid

The topic of internal gravity wave generation by oscillating bodies in density-stratified fluids has recently gained prominence owing to the importance of oceanic internal tides, generated by the oscillation of the barotropic tide over bottom topography, in the dynamics of the Earth-Moon system. To assess the role of the boundary condition at the body (in the ocean at the topography), we consider the only problem for which a full viscous solution is known: the oscillating circular disk. The inviscid theory, the full viscous theory (i.e. with viscous effects on both wave propagation and generation) and the partial viscous theory (i.e. with viscous effects on propagation alone) are compared with low-resolution conductimetric measurements from the literature and with new and original high-resolution PIV measurements. Viscous effects on propagation are required for prediction of the wave profiles; generation becomes free-slip at Stokes number over a million, and remains no-slip otherwise.