Asymmetric and axisymmetric dynamics of tropical cyclones

Abstract

We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3- D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized into annular rings, the azimuthally averaged heating rate and radial gradient thereof is considerably less than that in the AX model. This lack of organization results broadly in a slower intensification rate in the 3-D model and leads ultimately to a weaker mature vortex after 12 days of model integration. While azimuthal mean heating rates in the 3-D model are weaker than those in the AX model, local heating rates in the 3-D model exceed those in the AX model and at times the vortex in the 3-D model intensifies more rapidly than AX. Analyses of the 3-D model output do not support a recent hypothesis concerning the key role of small-scale vertical mixing processes in the upper-tropospheric outflow in controlling the intensification process. In the 3-D model, surface drag plays a particularly important role in the intensification process for the prototype intensification problem on meteorologically relevant timescales by helping foster the organization of convection in azimuth. There is a radical difference in the behaviour of the 3-D and AX simulations when the surface drag is reduced or increased from realistic values. Borrowing from ideas developed in a recent paper, we give a partial explanation for this difference in behaviour. Our results provide new qualitative and quantitative insight into the differences between the asymmetric and symmetric dynamics of tropical cyclones and would appear to have important consequences for the formulation of a fluid dynamical theory of tropical cyclone intensification and mature intensity. In particular, the results point to some fundamental limitations of strict axisymmetric theory and modelling for representing the azimuthally averaged behaviour of tropical cyclones in three dimensions.