Numerical modeling of a rotating cumulonimbus cloud

Abstract

The processes leading to the extreme concentration of vorticity that accompany the formation of a tornado are not well understood. One of the steps in this process appears to be the concentration and vertical propagation of available vorticity in a rotating mesoscale convective system. An attempt is made to understand the vorticity concentration process through a numerical study o f a two-dimensional, axisymmetric, and time-dependent model of a rotating convective cloud. The numerical model consists of the three equations of motion, a thermodynamic equation, a set of continuity equations for the water substances (water vapor, cloud water droplets, ice crystals, rain and hail), a diagnostic nondimensionalized pressure equation, and appropriate boundary conditions. These equations are solved numerically by use of centered differences in space and time on a 16 km by 16 km grid. The grid spacing is 500 m and most calculations use a time step of 1 second. Two experiments are performed in this study. A nonprecipitating cloud with rotation induced in the outer half of the domain is constructed. A precipitating cloud is also generated with the same characteristics of the previous cloud, except the autoconversion process is activated to produce precipitation-size hydrometeors. The numerical model produces features of convective clouds consistent with the two-dimensional axisymmetric model of Soong and Ogura (1973), although that model does not contain rotation. Furthermore, the present model extends the work of Leslie and Smith (1979) by the incorporation of cloud-microphysical processes and by the extension of the spatial dimensions. In experiments which examine both precipitating and nonprecipitating clouds, the vertical gradient in vertical velocity is accompanied by a radial inflow which is responsible for increasing the vorticity in the vicinity of the core of the cloud. In the precipitating case, drag created by the precipitation hydrometeors enhances the downdraft in the middle level of the domain. The transition region between this down-draft and the updraft found just above is accompanied by radial inflow which further increases the vorticity in the middle level of the domain, where Donaldson (1978) has observed the formation of the Mesoscale Vortex Signature.