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A minimal 3D numerical model designed for basic studies of tropical cyclone behavior is described. The model is formulated in coordinates on an f or ␤ plane and has three vertical levels, one characterizing a shallow boundary layer and the other two representing the upper and lower troposphere, respectively. It has three options for treating cumulus convection on the subgrid scale and a simple scheme for the explicit release of latent heat on the grid scale. The subgrid-scale schemes are based on the mass-flux models suggested by Arakawa and Ooyama in the late 1960s, but modified to include the effects of precipitation-cooled downdrafts. They differ from one another in the closure that determines the cloud-base mass flux. One closure is based on the assumption of boundary layer quasi-equilibrium proposed by Raymond and Emanuel.It is shown that a realistic hurricane-like vortex develops from a moderate strength initial vortex, even when the initial environment is slightly stable to deep convection. This is true for all three cumulus schemes as well as in the case where only the explicit release of latent heat is included. In all cases there is a period of gestation during which the boundary layer moisture in the inner core region increases on account of surface moisture fluxes, followed by a period of rapid deepening. Precipitation from the convection scheme dominates the explicit precipitation in the early stages of development, but this situation is reversed as the vortex matures. These findings are similar to those of Baik et al., who used the Betts-Miller parameterization scheme in an axisymmetric model with 11 levels in the vertical. The most striking difference between the model results using different convection schemes is the length of the gestation period, whereas the maximum intensity attained is similar for the three schemes. The calculations suggest the hypothesis that the period of rapid development in tropical cyclones is accompanied by a change in the character of deep convection in the inner core region from buoyantly driven, predominantly upright convection to slantwise forced moist ascent.

A simple two-layer analogue model is used to elucidate aspects of vortex motion in a vertically sheared zonal flow. The model is based on the idea that a vortex can be considered as the sum of a pair of barotropic vortices, one whose vorticity, or potential vorticity, resides in the upper layer and the other whose vorticity resides in the lower layer. Each vortex has an associated tangential velocity distribution in the other layer, which advects the vortex in that layer. The strength of this velocity distribution is characterized by a coupling parameter, which, in the case of quasi-geostrophic vortices, is related to the Rossby depth scale. Besides their mutual advection, the component vortices are differentially advected by vertical shear. The model leads to a set of coupled ordinary differential equations for the motion of each component vortex, which may be solved analytically in certain circumstances. The calculations indicate two types of flow behaviour according to the strength of the component vortices, the degree of vertical coupling and the strength of the shear. For weak shear and/or strong vortices and strong coupling, the vortices rotate around each other as their mean centre translates with a fraction of the mean zonal flow. For strong shear and/or weak vortices and weak coupling, the vortices undergo a partial rotation while they are in proximity, but become progressively separated by the shear. The calculations are an aid to understanding the range of behaviour of vortices in shear in numerical calculations by other authors, and it is reasonable to presume that the processes represented by the model are fundamental processes in tropical cyclones also.The analogue model is evaluated in the context of quasi-geostrophic theory, where the breakdown into the component vortices can be accomplished and where the complete problem can be solved numerically without approximation. The results of the quasi-geostrophic model are contrasted with those of other recent studies of baroclinic vortices in the absence of vertical shear.

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The motion of an initially symmetric vortex in a spatially‐varying large‐scale flow on a beta plane is investigated using a nondivergent, barotropic numerical model. The calculations extend those carried out for the case of zero basic flow in Part I. The large‐scale flows are provided by meridionally‐varying zonal flows, or single‐mode, stationary, finite‐amplitude planetary waves in a channel. Interest is focused on the evolution of vortex asymmetries and their role in determining vortex motion relative to the basic large‐scale flow. As in Part I, the calculations are used to assess averaging procedures for computing the environmental wind field of a tropical cyclone from observed wind data. It is shown that averaging over an annular region centred on the vortex is, in principle, more accurate when there is a basic flow, in comparison with the case of zero basic flow.