Tropical Cyclogenesis via Convectively Forced Vortex Rossby Waves in a Shallow Water Primitive Equation Model

Abstract

This work examines further the problem of tropical cyclogenesis by convective generation of vertical vorticity within a preexisting cyclonic circulation whose initial maximum tangential wind is approximately 5 m s⁻¹. This paper validates and extends recent work examining the suggested upscale cascade mechanism in a three-dimensional quasigeostrophic framework using a simple shallow water primitive equation (SWPE) numerical model and helps clarify certain aspects of the Rossby adjustment problem on a nonresting basic state for finite-amplitude nonaxisymmetric disturbances. The SWPE approach serves as a meaningful intermediate step between the quasigeostrophic and full-physics frameworks and allows a simple investigation of the effects of unbalanced dynamics (contributions of gravity waves) and Rossby numbers of order unity. The authors compare quantitative results of the two models on the storm spinup time and magnitude. For asymmetric initial conditions whose mass and wind field are out of balance, robust spinup is still obtained provided the initial asymmetries possess a significant vortical component. Episodic convective forcing parameterized via unbalanced vorticity anomalies is shown to lead to spinup of a tropical storm strength vortex on a timescale of approximately 40 h. When the convective vorticity anomaly has a large amplitude compared to the initial 5 m s⁻¹ basic-state vortex, the convective anomaly becomes the dominant or “master vortex,” remaining essentially intact and shearing the basic-state vortex. This behavior is understood heuristically in terms of a “vortex beta Rossby number,” which provides a local measure of the strength of the nonlinear terms in the vorticity equation compared to the corresponding linear vortex Rossby wave restoring term. Additional experiments show that, if the convection in a single pulse mode occurs in multiple patches (or“subclusters”) rather than in a single cluster with equal cyclonic circulation, a reduced spinup is obtained. This effect is captured in simulations with a nonlinear nondivergent semispectral model, establishing that gravity wave dynamics are not responsible for the reduction of spinup in the multiple-cluster case. A wave-mean-flow approximation with the nondivergent model also reproduces the effect of a reduced spinup with multiple-cluster convection. The applicability of the wave-mean-flow approximation at these finite amplitudes is explained by the fact that the vortex beta Rossby number of these configurations is not large. A case study using satellite observations shows that, although the observations are for a tropical storm rather than for genesis, an intensification mechanism similar to that discussed here is suggested. Further tests of the theory are proposed.