Applicationof theConcepts of Rossby Length andRossby Depth to Tropical Cyclone Dynamics

is paper examines the usefulness of the complementary concepts of Rossby length and Rossby depth. ese 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 coe›cients can be considered as constants, this elliptic partial dišerential equation for the transverse circulation is solved in three dišerent ways: (i) First perform a vertical transform to obtain a radial structure equation, from which arises the concept of a spectrumof Rossby lengths; (ii) First perform a radial transform to obtain a vertical structure equation, fromwhich arises the concept of a spectrum of Rossby depths; (iii) First solve the elliptic PDE directly, without regard to boundary conditions, and then enforce the boundary conditions using the method of image circulations. For weak vortices, Rossby lengths are large and Rossby depths are small, so that the secondary circulation is horizontally elongated and vertically compressed. For strong vortices, Rossby lengths are small and Rossby depths are large, so that the secondary circulation is more vertically elongated and so horizontally compressed that some of the eyewall updraŸ can return as subsidence in the eye. For strong vortices, the secondary circulation associated with eyewall diabatic heating can be signicantly suppressed by the large inertial stability in the interior of the vortex. e large variations of Rossby depth with vortex strength also have important implications concerning how far Ekman pumping can penetrate vertically; only strong vortices have large enough Rossby depths to allow Ekman pumping to penetrate deep into the troposphere.