On the Dynamics of the Formation of the Kelvin Cat’s-Eye in Tropical Cyclogenesis. Part I: Climatological Investigation

Abstract Motivated by Dunkerton et al., a climatological study of 54 developing easterly waves in 1998–2001 was performed. 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. Using a closed PV contour as a criterion for the formation of the cat’s-eye, it was shown that on average it takes ~2.6 days for open PV contours to transform to a closed coherent structure. Bootstrap analysis was then applied to determine the reliability of the easterly wave–like pattern in the composite perturbation PV analysis. It is suggested that the coexistence of a nonlinear critical layer and a region of weak meridional PV gradient over several days, found to occur in only ~25% of the easterly waves, might be a major factor to distinguish developing and nondeveloping disturbances. This finding may explain why only a small fraction of easterly waves contribute to tropical cyclogenesis. Additionally, an analytic time scale of the form was obtained, where Q is the mass sink, ε is the amplitude of the initial disturbance, and τ is 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 54 cases of easterly waves that developed into named storms, highlighting the importance of nonlinear and diabatic processes in cat’s-eye formation.