A numerical model consisting of three shallow, constant density layers is used to study fundamentals of the evolution of a hurricane-like vortex. Convection is represented in the model as mass source/sink terms for each of the layers. These source/sink terms represent the vertical redistribution of mass by convection. There is also an accompanying transfer of momentum between the layers via the mass flux terms. This convection scheme is based on the parameterization developed by Ooyama (1966) for three constant density layers and reinterpreted by Demaria and Pickle (1988) for an isentropic model.
The Ooyama/Demaria and Pickle (ODP) scheme relies mass being forced out of the boundary layer via frictionally driven horizontal convergence. A closure relation which specifies the mass transported into the upper layer of the model in terms of transport out of the sub-cloud layer is based on conservation of moist static energy in the upper layer.
Rather than specifying the mass flux out of the model boundary (sub-cloud) layer exclusively by frictionally driven horizontal convergence, we assume that the vertical mass flux is driven in part or entirely by destabilization of boundary layer through surface fluxes of latent and sensible heat. The convective updraft and accompanying downdraft are assumed to maintain the equivalent potential temperature of the boundary layer in a state of quasi-equilibrium as discussed by Raymond (1995). The surface flux of equivalent potential temperature defines an equilibrium mass flux and the actual mass flux adjusts to this equilibrium value over a finite time (assumed to be about 2 hours) as in Emanuel (1995). The ratio of updraft to downdraft is given in terms of a precipitation efficiency which depends on the vertical moisture profile and the net vertical transport allows the equivalent potential temperature to vary in each layer.
Evolution of model vorticies with and without frictionally forced convergence out of the boundary layer are compared. This convective scheme allows a direct comparison of the effect of large scale convergence and boundary layer destabilization on the growth rate and eventual structure of the model vortices.