Multi-Scale Asymptotics for Strongly Tilted Tropical Vortices

The asymptotic theory for three-dimensional vortices in the gradient wind regime by Paeschke et al. (2012), JFM, vol. 701, 137--170 is revisited. The theory considers vortices that are nearly axisymmetric at each vertical level but involve relative horizontal displacements of the vortex centerline comparable to the vortex diameter. This justifies the notion of “strong tilt” and implies that tilted configurations of tropical storms as reported, e.g., by Duncerton et al. (2009), Atmos. Chem. Phys., 9, 5587--5646, are covered by the theory. By definition, the gradient wind regime amounts to vortex Rossby numbers of order unity only, however, such that vortices of hurricane strength are not in reach of the original derivations.

The first part of the proposed presentation reports on an extension of the theory to the cyclostrophic, low Froude number regime corresponding to hurricane strengths H1, H2 on the Saffir-Simpson scale. With this extension, large vortex Rossby numbers and the regime of tropical storm-to-hurricane transitions can be addressed. The analysis reveals that purely asymmetric diabatic heating that would not give rise to any secondary circulation can intensify a vortex as efficiently as axisymmetric forcing, provided the circumferential first Fourier mode heating component aligns appropriately with the vortex tilt. Agreement of these results with Lorenz’ classical theory of the available potential energy (APE) budget under diabatic processes is demonstrated.

The second part of the presentation will report on current research work aiming at the asymptotically consistent incorporation of boundary layer processes and of organized deep convection in the theory. Under investigation are single- vs. multideck boundary layer representations, related matching conditions that connect the boundary layer and bulk vortex flows, the ventilation of the boundary layer by deep convection, and the local structure of individual hot towers.