Two-dimensional convection in non-constant shear: a model of mid-latitude squall lines

Abstract

Numerical simulations of two-dimensional deep convection are analysed using analytical models extended to include shallow downdraughts and non-constant shear. The cumulonimbus are initiated by low-level convergence created by a finite amplitude downdraught. These experiments have constant low-level shear and differ only in the profile of mid-and upper-level winds. Quasi-steady convenction is produced if the mid- and upper-level flow has small shear and the low-level shear is large. The surface precipitation ismaximized for no intial relative relative flow aloft, if stationary, this storm (P(O)) can give prodigious locilized rainfall; P(O) is the two-dimentisonal equivalent of the supercell. These results are placed in context with previous two-dimensional simulations. Attention is drawn to the similiarity with previous two-dimensional simulations. Attention is drawn to the similarity with squall lines in central and eastern U.S.A. Storm P(O) is analysed by construction of time-averaged fields of streamfunction, vorticity, teperature, and height deviation. The smoothness of these fields suggests a conceptual model of the storm dynamics which involves cooperation between distinct charcteristic flows; an overturning updraught, a jump type updraught, a shallow downdraught, a low-level rotor, and a boundary layer. An idealized analytical model is described by solution of the equations for steady convection. These solutions, for the remote flow, are derived from energy conversation, mass continuity and a momentum budget, and they give relationships between the non-dimensional parameteres of the problem. It is apparent that the convection is a high Froude (or low Richardson) number flow demanding the existence of a cross-storm pressure gradient. Inherent in this idealized model is a vortex sheet between updraught and down-draught and it is considered that the dynamical instability of this sheet is related to complexities in the numerical simulation. Furthermore, these results show that in two-dimensions both non-constant shear and a shallow downdraught are necessary to maintain steady convection.