AN ANALYTICAL APPROACH TO THE NONLINEAR DYNAMICS OF MOIST FRONTOGENESIS

The existence of analytical solutions for two-dimensional nonlinear se migeostrophic models of moist frontogenesis is investigated. Two diffe rent schemes for the modeling of stratiform cloud thermodynamics are t aken into account, one based on the assumption of an everywhere cloudy environment, while in the other the atmosphere is considered to be ex actly saturated and only condensation effects are relevant. In the fir st case, an exact analytical solution is derived for arbitrary boundar y conditions, which satisfies the requirements for the validation of t he semigeostrophic approximation even when the atmosphere is condition ally unstable with respect to slantwise convection. The growth of symm etric instabilities with no short-wave cutoff is predicted for this co nditionally unstable atmosphere, even under the approximations of the semigeostrophic theory. An analogous, but approximate, analytical solu tion is then proposed for the second case. The errors introduced by th e approximation are, however, not bigger than the terms neglected in t he semigeostrophic approximation itself.