A steady nonlinear and singular vortex Rossby wave within a rapidly rotating vortex. Part II: Application to geophysical vortices

In a previous paper, Caillol [Geophys. Astrophys. Fluid Dyn., 2014, 108] investigated the steady nonlinear vortical structure of a singular vortex Rossby mode that has survived to a strong critical-layer-like interaction with a linearly stable, columnar, axisymmetric and dry vortex. We presented a general theory for this wave/mean flow interaction through the nonlinear critical layer theory and calculated the mean azimuthal and axial winds induced at the critical radius at the end of this interaction in the final stage. We here apply that theory to rapidly rotating geophysical vortices: tropical cyclones, cold-air mesocyclones and tornadoes. We find that the numerous assumptions invoked in that paper agree well with the reality of those intense vortices. We also find that in spite of a lack of moist-convection modelling, this dry vortex is fairly well accelerated at the critical radius by such a shear wave with a magnitude of order the square root of the damped-wave amplitude. The intensification level strongly depends on the aspect ratio, height of the system: rapid vortex and parent vortex, over core radius. The thinner the vortex is, the sharper the intensification is. This result is in sharp contrast to the numerous numerical simulations on VR wave/vortex interactions that yield a much smaller intensification of order the square of the wave amplitude. This weakly nonlinear approach nevertheless fails to model small vertical wavelength VR wave/vortex interactions for their related asymptotic expansions are divergent and for they yield strongly nonlinear VR waves coupled with evolving critical layers whose extent can no longer be considered as thin.