Synthesis of Vortex Rossby Waves. Part I: Episodically Forced Waves in the Inner Waveguide

Spiral cloud bands dominate tropical cyclones' appearance in satellite and radar images. It is generally accepted that at least some of them are vortex Rossby waves that propagate on the radial gradient of mean-flow-relative vorticity. This study models these features in Fourier and time domains as linear, barotropic, nondivergent waves on a maintained mean vortex scaled to resemble tropical cyclones. This formulation is the simplest one imaginable that encompasses the essential rotational dynamics. The modeled waves are episodically forced by a rotating annular train of sinusoidal vorticity sources and sinks that crudely represents eyewall convection. Substantial quiescent time intervals separate forced intervals. The waves propagate wave energy predominantly outward and converge angular momentum inward. Waves' energy is absorbed as their perturbation vorticity becomes filamented near the outer critical radii where their Doppler-shifted frequencies and radial group velocities approach zero. The waves can propagate spatially only in narrow annular waveguides because of their slow tangential phase velocity and the restricted Rossby wave frequency domain. Although radial shear of the mean flow distorts their velocity field into tightly wound spirals, their streamfunction and geopotential fields assume the form of elliptical gyres or broad trailing spirals that do not resemble observed hurricane rainbands.