Two‐dimensional convection in non‐constant shear: A model of mid‐latitude squall lines

Abstract

AbstractNumerical 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.