Organization of mesoscale convective systems: 2. Linear theory

Abstract

The anelastic system of equations (3‐D momentum, continuity and thermodynamic energy) is used to investigate the organization of mesoscale convective systems (MCSs) using the reference layer concept presented in part 1. Latent heating is assumed to be proportional to the vertical velocity. The WKBJ method is used to solve this system of equations by perturbing the solution linearly from that at the reference level, which is the top of the reference layer. The reference layer is defined as a layer with maximum wind shear and unstable moist stratification over a minimum thickness of 200 mbar. The characteristics of the reference layer, such as the magnitude of the shear and moist stratification, determine the type of MCS' organization and associated properties in the analysis. This result agrees well with numerical simulations of linear MCSs presented in part 1 of this series of study. Three types of MCSs are identified from the linear theory: one is nonlinear and two are linear. The group speed of all three types turns out to be proportional to the mean wind at the reference level. Nonlinear MCSs occur when the vertical wind shear is weak and the stratification is unstable. Type 1 linear solutions are neutral, shear‐parallel lines; their reference layers are usually in the middle troposphere. Type 2 linear solutions are amplifying, shear‐perpendicular lines; their reference layers are usually in the lower troposphere. The theory predicts the widths and growth rates of the type 2 linear MCSs. The width of an amplifying MCS is determined as a simple function of the Richardson number, while the growth rate is a function of vertical wind shear and Richardson number. Tests of the linear theory using data from several field experiments show that it gives fairly realistic results for a variety of the observed MCSs.