Direct numerical simulation of internal gravity wave attractor in trapezoidal domain with oscillating vertical wall

Abstract

Direct numerical simulation of internal gravity waves focusing and developement of a wave attractor was performed with the help of two different numerical approaches. Mathematical formulation corresponds to experiments on exitations of inner waves in a trapezoidal container with salt solutions through forced oscillations of the left boundary. It was shown that numerical simulations reproduce the experiments after taking into account ther imperfection of linear salinity profile near the upper boundary. The amplitudes of resulting oscillations in both numerical simulations are increased as compared to the experiments due to loss of energy of the 3D wave generator in the experiments. Despite the fact that the general shape of the attractor is reproduced by both method, there are differences in velocity profiles near the left boundary. This fact requires further investigations since this discrepancy may in influence nonlinear dynamics of developing instabilities.