The concepts of Rossby length and Rossby depth and their application to hurricane dynamics

This study examines the usefulness of the complementary concepts of Rossby length and Rossby depth. These concepts are discussed in the context of idealized analytical solutions of the transverse circulation equation that arises in the balanced vortex model of tropical cyclones. When its coefficients can be considered as constants, this elliptic partial differential equation for the transverse circulation can be solved in three different ways: (i) First perform a vertical transform to obtain a radial structure equation, from which arises the concept of a spectrum of Rossby lengths; (ii) First perform a radial transform to obtain a vertical structure equation, from which arises the concept of a spectrum of Rossby depths; (3) Solve the elliptic PDE via the Green's function and enforce the lower boundary condition using the method of images. For weak vortices, Rossby lengths are large and Rossby depths are small, so that the central symmetry condition plays a strong role while the top and bottom boundary conditions play a weak role. For strong vortices, Rossby lengths are small and Rossby depths are large, so that the central symmetry condition plays a weak role while the top and bottom boundary conditions play a more important role. For strong vortices, the secondary circulation associated with eyewall diabatic heating can be significantly suppressed, while the interior circulation associated with Ekman pumping can penetrate deep into the troposphere.