A numerical modelling study of the geostrophic adjustment process following deep convection

A high resolution numerical model based on the anelastic equations of motion is used to simulate the geostrophic adjustment process that follows the growth of a single, deep convective plume. Interest focuses on the form of the balanced state and the proportions of energy which go into gravity waves, dissipation and balanced flow. Three simulations are described: a non-rotating case, an intermediate rotation case (f= 10−3S−1) and a high rotation case (f= 2 × 10−3S-1). The use of these artificially high rotation rates (in the context of the terrestial atmosphere) is regarded as a device for shortening the adjustment time thereby rendering the objective of the study computationally feasible. The model simulations are two-dimensional and use an idealized specification of the moist process in which precipitation is instantaneous and no cloud is permitted. The initial state of the model atmosphere is calm and horizontally-stratified except for a warm, moist bubble near the surface. Integrations are carried out for 50000 s by which time quasi-steady flow states are achieved. In the rotating cases, the final quasi-balanced state takes the form of a well-defined lens-shaped region of uniform absolute momentum at the neutral buoyancy level and an intense, vertical shear line front extending upwards from the surface. The response is characterized by two length scales: the Rossby radius of deformation based on the depth of the convection, and a mesoscale cloud scale related to the amount of mass which convects and the rotation rate, amongst other factors. It is found that - 30% of the kinetic energy released in convection is captured in balanced flow- considerably larger than indicated in earlier studies and not dependent on the high rotation rates used here. Simple scaling arguments are used to account for the efficiency of balanced energy retention as a function of the amount of mass that convects and to define an upper bound on the amount of mass that can be convected through a single plume in a rotating environment. This is tentatively identified with a maximum possible scale for mesoscale convective systems. An analytic model for the balanced state is presented and shown to fit the simulated flow very well. The success of this model underlines the secondary role played by mixing in the numerical model.