Slumping of non-Boussinesq density currents of various initial fractional depths: a comparison between direct numerical simulations and a recent shallow-water model

Simulations of non-Boussinesq density currents of various initial fractional depths are performed, and a detailed comparison with a recent shallow-water model [18] is done for a wide range of density ratio 10̄4 ≤ ρc/ρa ≤ 104 and initial depth ratio 1 ≤ H* ≤ 50 in the regime of constant-speed initial phase. Good agreement is observed in a large region of the parameter space. The larger discrepancy is observed in the range of high H* and low-ρc/ρa for which the shallow-water model overpredicts the velocity of the current. Two possible reasons are suspected, namely the fluid motion in the ambient fluid which is not accounted for in the model, and the choice of the model for the front condition.