Evaluation of the theoretical speed and depth of gravity currents using three-dimensional numerical simulations

In a recent article, Bryan and Rotunno (2008, JAS) extended the analytic theory for gravity currents to include variations in density with height. The resulting equations are more applicable to gravity currents (i.e., cold pools) in the Earth's atmosphere, and are thus more applicable to mesoscale convective systems. They found that the propagation speed is ~25% slower and the maximum possible depth is ~35% shallower than results from the classic incompressible (constant density) theory.

One uncertain aspect of the theoretical results is the role of viscosity. Most studies in the severe storms community have used the inviscid equations, which yield the maximum possible cold pool depth. However, Benjamin (1968, JFM) argued that this state is "difficult, if not impossible" to achieve; instead, he argued that the maximum possible energy dissipation rate (using the viscous equations) yielded the likely maximum cold pool depths.

In order for these results to be applied to observed convective systems, more guidance is necessary. Three-dimensional large-eddy simulations are used to help solve this dilemma. Results support Benjamin's viewpoint, and suggest that inviscid solutions are not relevant to atmospheric cold pools.