The optimal state for gravity currents in shear

This study examines the lifting of sheared environmental air by gravity currents, focusing primarily on thetheoretical ''optimal state'' in which near-surface flow is turned into a vertically oriented jet. Theoreticalmodels are presented from multiple perspectives, including the vorticity perspective that was first presentedby Rotunno, Klemp, and Weisman and a flow-force balance perspective based on conservation of mass andmomentum. The latter approach reveals a constraint on the depth of the environmental shear layer relative tothe 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 isnearly (although not strictly) vertical. Then, by initializing a time-dependent numerical model with a stagnantcold pool in an environment with low-level shear, it is shown that a statistically steady flow can be maintainedwith all the important elements of the analytic solution. Most notably, the front-relative flow is negligiblebehind the surface gust front at all levels, the interface of the cold pool maintains a predominantly verticalstructure, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontalflux of environmental vorticity on the side of the control volume. Sensitivity simulations confirm thatthe constraints identified by the analytic study must be met for the optimal state to be realized and that liftingof near-surface environmental air is optimized when a vertically oriented jet is created and maintained.