On the dynamics of the formation of the Kelvin cat's eye in tropical cyclogenesis

This study brings new understanding on easterly waves that develop into named storms over the Atlantic and eastern Pacific. It has recently been shown that these storms are almost all associated with a cyclonic Kelvin cat's eye of a tropical easterly wave critical layer, located equatorward of the easterly jet axis. To better understand the dynamics of tropical cyclogenesis, the flow characteristics and the physical and dynamical mechanisms for the formation of the cat's eyes are investigated. A climatological study of 54 developing easterly waves in 1998-2001 was conducted using ECMWF reanalysis data. Time-lagged composites in a translating reference frame following the disturbances indicate a weak meridional potential vorticity (PV) gradient of the easterly jet, and a cyclonic critical layer located slightly to the south of the weak PV gradient, consistent with previous findings in the marsupial paradigm. In addition, the statistically significant pattern of developing and non-developing PV anomalies in the composite shows that the coexistence of a nonlinear critical layer and a region of weak meridional PV gradient over several days occurs in only ~25% of the easterly waves. This finding may explain why only a small fraction of easterly waves eventually develop into tropical storms. Moreover, we obtained an analytic time scale of the form τe^τQ~O(ε^(-1)) with Q being the mass sink, ε the amplitude of the initial disturbance, and τ the cat's eye formation time, that governs the onset of nonlinearity for forced disturbances on a parabolic jet critical layer. This time scale is consistent with that found in the 54 cases of easterly waves that developed into named storms, highlighting the importance of nonlinear and diabatic processes in cat's eye formation. A shallow water model is then used to study forced and unforced problems of disturbances on a parabolic jet and the observed jet in the composite. The nonlinear forced simulations, with the convective heating represented by a mass sink, produced a realistic time scale for cat's eye formation, and confirm our above-mentioned analytic solution. These results confirm 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 formation of the cat's eye in tropical cyclogenesis.