The Optimal State for Gravity Currents in Shear

Abstract

Abstract This study examines the lifting of sheared environmental air by gravity currents, focusing primarily on the theoretical “optimal state” in which near-surface flow is turned into a vertically oriented jet. Theoretical models are presented from multiple perspectives, including the vorticity perspective that was first presented by Rotunno, Klemp, and Weisman and a flow-force balance perspective based on conservation of mass and momentum. The latter approach reveals a constraint on the depth of the environmental shear layer relative to the depth of the cold pool. Based on these control-volume constraints, a numerical solution for steady, inviscid, isentropic flow is obtained that shows how the cold-pool interface has a slightly concave shape and is nearly (although not strictly) vertical. Then, by initializing a time-dependent numerical model with a stagnant cold pool in an environment with low-level shear, it is shown that a statistically steady flow can be maintained with all the important elements of the analytic solution. Most notably, the front-relative flow is negligible behind the surface gust front at all levels, the interface of the cold pool maintains a predominantly vertical structure, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontal flux of environmental vorticity on the side of the control volume. Sensitivity simulations confirm that the constraints identified by the analytic study must be met for the optimal state to be realized and that lifting of near-surface environmental air is optimized when a vertically oriented jet is created and maintained.