An analytical model of the balanced flow created by localized convective mass transfer in a rotating fluid

Abstract

Abstract A class of exact analytic solutions is presented which represent the steady flow which persists after a finite region of stratified fluid is displaced vertically under the action of non-entraining, moist convection. In this process, the absolute momentum and equivalent potential temperature are imagined to mix within the convecting fluid so that the end state has constant absolute momentum and (dry) static stability. The balanced flow that remains consists of a vertical shear-line front in the region from which the fluid was withdrawn and a lenticular region characterized by zero absolute vorticity with adiabatic warming below and cooling above. The form of this lens-front configuration changes depending on the amount of mass that is assumed to convect. A contour integration technique for evaluating the total energy of this class of solution is presented. Simple asymptotic expressions for the energy may be obtained for large lens-front separation and if the initial convective available potential energy is known, an upper bound can be deduced for the total amount of mass that can convect through a single plume. This limit, together with the Rossby radius of deformation based on the depth of the convection, defines two fundamental length scales.