_{0}. For outwardly decreasing ζ

_{0}, the VRWs have Doppler-shifted frequency Ω < 0 so that their intrinsic phase propagation is inward and upstream against the faster mean flow. Under this paradigm, VRWs initiated by convection in the eyewall propagate wave energy outward, but converge angular momentum inward. The VRWs thus can pump cyclonic angular momentum from outside the eye inward toward the radius of maximum wind. The outward propagating wave energy is absorbed in the neighborhood of a critical radius where Ω = 0.The inward wave angular momentum flux is thus divergent around the critical radius and convergent at the locus of forcing. This mechanism may force initiation of outer wind maxima by decelerating the mean flow inward from the critical radius, leading (in nature or full-physics models) to frictional convergence that localizes convection there. VRW propagation is confined to an annular waveguide bounded by the outer critical radius and an inner radius where Ω = Ω

_{c}, the Rossby-wave cutoff frequency. Because of VRW's slow phase propagation and the narrow interval Ω

_{c}< Ω < 0, the waveguide has limited (10s of kilometers) radial extent.

Here, VRW excitation in a barotropic nondivergent model is represented as a Fourier series with brief episodes of active forcing separated by much longer quiescent intervals. During the active intervals, the streamfunction appears as broad elliptical gyres even though the vorticity quickly wraps into narrow trailing spirals. As the forcing diminishes and the waves propagate outward, the streamfunction briefly transforms into realistic trailing spirals. The wave energy accumulates near the critical radius because the group velocity is so slow there.

Paradoxically, the most recognizable VRW filamentation and axisymmetrization also takes place near the critical radius where the waves are acting to decelerate the mean flow. Then, as the vorticity axisymmetrizes into tightly wound filaments of alternating polarity, the streamfunction amplitude decays quickly. The streamfunction looks like spiral bands observed in TCs only during the brief interval after gyres have distorted into spirals, but before axisymmetrization eats them up.