Dynamics of the optimal state for cold pools in shear

This study examines the dynamics of cold pools when they spread into environments with vertical wind shear, focusing specifically (for this presentation) on the theoretical "optimal state" in which the sheared environmental flow is turned into a vertically oriented jet. Steady analytic solutions are presented from two perspectives: 1) the vorticity perspective, which was first presented in an article by Rotunno, Klemp, and Weisman; and 2) the flow-force-balance perspective, based on conservation of mass and momentum. The latter perspective reveals previously undocumented constraints on the depth of the environmental shear layer. In support of the analytic solutions, numerical simulations of cold pools in shear are also examined. The initial conditions include the aforementioned constraint on shear layer depth. It is shown that a statistically steady flow can be maintained with all the important elements of the theoretical solution. Most notably, the front-relative flow is negligible at all levels behind the surface gust front, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontal flux of environmental vorticity on the right side of the control volume.