A numerical study of temporal shallow mixing layers using BGK-based schemes

A numerical study of the temporal shallow mixing layers is performed. The depth-averaged shallow water equations are solved by the finite volume method based on the Bhatnagar–Gross–Krook (BGK) equation. The filtering operation is applied to the governing equations and the well-known Smagorinsky model for the subgrid-scale (SGS) stress is employed in order to present a large eddy simulation (LES). The roll-up and pairing processes are clearly shown and the corresponding kinetic energy spectra are calculated. The effects of the Froude number and the bottom friction are numerically investigated. It is shown that the growth rate of the mixing layer decreases as the Froude number increases, which is very similar to the compressible mixing layers when considering the effects of the Mach number. The numerical results also indicate that the increase in bottom friction can enhance the stability of the flows, which is physically reasonable and consistent with the theoretical and experimental findings.