An Analytical Solution to the Perturbation Analysis of the Interaction between Downburst Outflows and Atmospheric Boundary Layer Winds

Abstract

Downbursts are negatively buoyant downdrafts that emerge from a storm and spread outward upon hitting the surface. The produced outflow, however, is not spreading through a calm environment, but rather through an atmosphere characterized by larger scale atmospheric boundary layer (ABL) winds. This interaction between ABL winds and downbursts forms an outflow that is more complex than an outflow created by an isolated downdraft. Here, we propose an analytical solution of the interaction between the ABL winds and an isolated downburst outflow. The model is applicable when the ratio of centerline downdraft velocity to the horizontal ABL velocity at the cloud base is larger than the nondimensional group: (H/D)(r/H)1.1, where H is the cloud base height, D is the diameter of the downdraft, and r is the distance from the centerline of isolated downdraft. Also, the solution is derived for specific direction in the outflow when the ABL winds and the isolated downburst outflow are aligned and the vertical profiles of radial velocity are self-similar. The model is based on the use of impinging jet dynamics, their spreading rates, and a universal renormalization group that describes numerous laboratory measurements of velocity profiles of impinging jets issuing into both quiescent and crossflowing backgrounds. The model assumes a “known” base state corresponding to an isolated downburst, and then derives its interaction with ABL winds by way of perturbation analysis. The radial and vertical profiles of horizontal velocity from our analytical model are compared against field observations of actual downbursts and other analytical models and physical simulations of downburst-like outflows.