Gradient Imbalance at the Outflow of Idealized Tropical Cyclone in a Three Layer Moist Neutral Model

Previous idealized models for Tropical Cyclones (TC) assume that the gradient wind balance holds everywhere in the free atmosphere (Charney and Eliassen, 1964; Ooyama, 1969; Emanuel, 1986). Since the gradient wind balance is by definition not divergent, this assumption (of gradient wind balance) makes the dynamics of the free atmosphere slave to the thermodynamics and momentum balance of the boundary layer. Here, a novel, three-layer, pressure coordinates model that avoids the assumption of (non-divergent) gradient wind balance and consistently accounts for surface pressure tendency is formulated. This model has explicit mass and momentum fluxes between the layers as well as explicit (reversible) thermodynamics. The convection in the free atmosphere is assumed as moist neutral with a parameterization that relaxes the temperature profile to a state of radiative convective equilibrium at a prescribed timescale. Boundary layer moisture budget is explicit as in Ooyama (1969) and Emanuel (1986). The model is accompanied by a derivation of conservation laws, which are used in order to interpret the effects of the local and global energy balances on the surface pressure tendency. We use this model in order to study the structure of a highly idealized axi-symmetric TC and examine the effect of upper level gradient imbalance and associated wind divergence on the TC intensity.