Analytical Solutions of Emanuel's Model of Precipitating Convection

Abstract

The fastest growing modes in Emanuel's recent model of inviscid precipitating convection in a saturated atmosphere with no shear have large horizontal wavenumbers, permitting a simple analytical analysis of their phase speed, growth rate, and modal structure as functions of the model parameters. It is found that the fastest growing modes are always localized near the ground, are slightly sloped, and grow almost as fast as if precipitation were to fall instantly to the ground. In any wind profile with weak unidirectional shear, rolls aligned along the shear vector grow fastest.