The propagation speed of gravity currents in a deep anelastic atmosphere

This study presents analytic solutions for the propagation speed of gravity currents using the deep anelastic equations. We compare these new results to the classic results that were based on the incompressible equations. Our main conclusion is that gravity currents propagate slower in a deep anelastic atmosphere. For typical conditions that are associated with mesoscale convective systems in the central United States, we find that propagation speed is approximately 25% slower than the classic propagation speed derived from the incompressible equations. To evaluate our analytic results, we conduct two-dimensional simulations of gravity currents. The simulations support the theory well. Furthermore, the simulations support the notion that there is a likely maximum cold pool depth that corresponds to the maximum dissipation rate realizable in steady flow.