Application of the Concepts of Rossby Length and Rossby Depth to Tropical Cyclone Dynamics

Abstract

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 di erential equation for the transverse circulation is solved in three di erent 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; (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 updra 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.

Global cloud-permitting simulations of Typhoon Fengshen (2008)

“…As a result, Γ in the middle troposphere was smaller in E_mp2 and E_mp4 than in N_mp2 (Fig. 4f ), and the Rossby depth (=1/(Γk); k is the radial wave number), which represents the vertical size of the forced circulation (Schubert and McNoldy 2010), in E_mp2 was approximately 1.6 times that in N_mp2. This elucidates the subsequent coupling of the large-scale lower and middle tropospheric vortices in E_mp2, which was substantially weaker in N_mp2.…”

Mechanism Governing the Size Change of Tropical Cyclone-Like Vortices

“…We may expect that the radial extent, or more precisely, the e-folding scale of SC, can be estimated as the local Rossby radius of deformation, ND/I, where N and D are buoyancy frequency and the vertical scale of the vortex, respectively (e.g., Schubert and McNoldy 2010). However, the local Rossby radius of deformation is found to be larger compared with the radial extents of SC realized in the model by around a factor of 2, even when we consider the radial variation of I.…”

Passive Microwave Quantification of Tropical Cyclone Inner-Core Cloud Populations Relative to Subsequent Intensity Change

“…Clouds and precipitation exist within the ascending branch of the secondary circulation, and are associated with intensification via the following processes: maintenance and strengthening of the warm core via diabatic and adiabatic warming (e.g., Schubert and Hack 1982;Vigh and Schubert 2009;Harnos and Nesbitt 2016), convergence driving vorticity aggregation and upscale growth (e.g., Hendricks et al 2004;Nguyen et al 2008;Wang 2014;Harnos and Nesbitt 2016), and moistening of the inner core for subsequent convective development (e.g., Bister and Emanuel 1997;Wang 2014;Harnos and Nesbitt 2016). Cloud modes encompassing predominantly liquid processes (i.e., shallow cumuli and cumulus congestus) and those containing both liquid and frozen hydrometeors (i.e., deep convection and stratiform clouds) occur in the tropics , while limited quantitative study of these cloud populations has taken place within TCs.…”