The dynamical structure of two‐dimensional steady convection in constant vertical shear

Abstract

AbstractA nonlinear regime of two‐dimensional steady convection in unidirectional flow of constant vertical shear is examined theoretically, the main objective being to determine the organization of the updraught and downdraught system. The asymptotic solution for the travel speed of the system and the remote flow obtained by Moncrieff and Green is used as lateral inflow and outflow boundary conditions. The internal flow and the shape of the interface separating the updraught and downdraught branches of the circulation are determined as solutions of a free‐boundary problem. The orientation of the flow is basically determined by the ratio of convective available potential energy (CAPE) to the square of the cloud layer shear expressed as R=CAPE/½ (Δ U)2. In all realistic ranges of R the interface slopes downshear, the slope being little affected by compressibility, by the negative vorticity generated in an interfacial boundary layer and by different values of R in the updraught and downdraught branches. Quasi‐steady storms are thus not adequately described by two‐dimensional dynamics. Certain three‐dimensional effects appear essential to significantly advance the theory of severe storms, and these are discussed with reference to existing numerical and observational models. Steady convection can exist only if the values of R in the updraught and downdraught branches lie within a limited range, a result of considerable significance in cloud physical terms.