Application of the Energy-Casimir Method to the Study of Mesoscale Disturbance Stability

Taking into account the effect of moisture, we derive a three-dimensional pseudoenergy wave-activity relation for moist atmosphere from the primitive zonal momentum and total energy equations in Cartesian coordinates by using the energy-Casimir method. In the derivation, a Casimir function is introduced, which is a single-wlue function of virtual potential temperature. Since the pseudoenergy wave-activity relation is constructed in the ageostrophic and nonhydrostatic dynamical framework, it may be applicable to diagnosing the stability of mesoscale disturbance systems in a steady-stratified atmosphere. The theoretical analysis shows that the wave-activity relation takes a nonconservative form in which the pseudoenergy wave-activity density is composed of perturbation kinetic energy, available potential energy, and buoyant energy. The local change of pseudoenergy wave-activity density depends on the combined effects of zonal basic flow shear, Coriolis force work and wave-activity source or sink as well as wave-activity flux divergence. The diagnosis shows that horizontal distribution and temporal trend of pseudoenergy wave-activity density are similar to those of the observed 6-h accumulated surface rainfall. This suggests that the pseudoenergy wave-activity density is capable of representing the dynamical and thermodynamic features of mesoscale precipitable systems in the mid-lower troposphere, so it is closely related to the observed surface rainfall. The calculation of the terms in the wave-activity relation reveals that the wave-activity flux divergence shares a similar temporal trend with the local change of pseudoenergy wave-activity density and the observed surface rainfall. Although the terms of zonal basic flow shear and Coriolis force contribute to the local change of pseudoenergy wave-activity density, the contribution from the wave-activity flux divergence is much more significant.