On the Dynamics of the Formation of the Kelvin Cat’s-Eye in Tropical Cyclogenesis. Part II: Numerical Simulation

A shallow-water model is used to study the role of critical layers in tropical cyclogenesis. Forced and unforced problems of disturbances on a parabolic jet associated with weak basic-state meridional potential vorticity (PV) gradients, leading to Kelvin cat’s-eye formation around the jet axis, are first investigated. Numerical simulations with various initial disturbance magnitudes and structures suggest that the results of previous studies can be extended to the next level of complexity toward the more realistic atmosphere. The model is therefore initialized using an observed jet profile obtained from the reanalysis data presented in Part I of this study. For this asymmetric marginally stable basic-state profile, unforced (free) and forced linear integrations show spatial contraction of the perturbation structures in the meridional direction, similar to what occurred in experiments on the parabolic jet. Nonlinear free simulations highlight the role of nonlinear processes in redistributing PV within the critical-layer region. However, they do not yield a realistic time scale for the formation of the cat’s-eye. By including diabatic heating as a mass sink term to represent convective PV generation, the nonlinear forced simulation is found to produce a realistic time scale for cat’s-eye formation, and confirms the analytical solution of τeτQ ~ O(ε−1) obtained in Part I. These results highlight the synergic role of the dynamical mechanisms, including wave breaking and PV redistribution within the nonlinear critical layer characterized by weak PV gradients and the thermodynamical mechanisms such as convectively generated PV anomalies in the cat’s-eye formation in tropical cyclogenesis.