A conservative, physically compatible discretization for turbidity currents

The recently introduced Mass Energy Enstrophy and Vorticity conserving (MEEVc) scheme for Navier-Stokes equations in 2D is extended to address turbidity currents. The structure preserving properties of the original scheme are preserved and a correct energy transfer is obtained for turbidity currents. The properties of the proposed discretization are proved and numerical results are presented. A comparison with literature results shows the ability of the new method to produce similar results with $10^2$ less degrees of freedom.