*f*-plane. The forcing approximates as Tropical Cyclone (TC) eyewall convection, mass source-sink pair that rotates with a specified cyclonic frequency, ω. The mean, axially symmetric vortex has a Wood-White profile with 50 m/s maximum winds at 25-km RMW. By default, ω is set to a quarter of the angular velocity at the RMW, V

_{0}/r.

A pair of rotating asymmetries with opposing polarity form near the core and have maximum amplitudes at the forcing locus. Excited VRWs propagate upon the mean vortex’s negative radial vorticity gradient within an “inner waveguide” confined between an inner turning point and outer critical radius. These boundaries correspond to the VRW cutoff and zero frequency, respectively. The former is the frequency of a one-dimensional VRW, expressed as the product of radius and the mean vortex radial vorticity gradient. It represents the greatest (most negative) frequency a VRW can assume. Therefore, the inner waveguide only can support a select range of VRWs propagating with a negative Doppler-shifted frequency: Ω = ω - V_{0}/r.

The waves propagate away from the forcing locus with an upstream (negative) phase velocity and downstream (positive) group velocity, relative to the vortex’s mean swirling flow. Initially inward propagating VRWs are Doppler-shifted to the cutoff frequency, become radially long and reflect from this turning point a few kilometers inward from the RMW, then move outward to the critical radius where they are ultimately absorbed and their energy is transferred to the mean flow. This is accompanied by a positive (outward) geopotential flux from the RMW that convergences at the critical radius. The critical radius is the locus where the VRW group velocity and Doppler-shifted frequency approaches zero. This causes vorticity to accumulate at the waveguide’s outer boundary and become tightly wound, filamented trailing spirals that wrap around the vortex core cyclonically to resemble observed TC rainbands on radar. The vortex axisymmetrize with time.

Forced VRWs also converge angular momentum into the RMW, thus accelerating the mean flow and intensifying the vortex. Between the forced asymmetries and critical radius, numerous vorticity filaments appear, indicating outward VRW propagation. Beyond the critical radius is the evanescent region where some wave energy leaks out and decays exponentially. The vortex follows a trochoidal track low speed with frequency ω, plausibly simulating eye wobbling observed in real TCs. Translation through the quiescent environment causes a slipstream flow that feeds angular momentum into the critical radius. It also interacts with the vortex’s mean swirling flow to form an outer streamfunction dipole of large, cyclonically curved gyres that rotate faster than V_{0}/r.

Vortex motion arises from the counterflow between the streamfunction asymmetries that advects vorticity across the vortex center, analogous with the beta gyres. Translation speed and trochoidal track amplitude are modulated by ω – low values (i.e., ≤0.25V_{0}/r) decrease speed but broaden the track, and vice-versa. Waveguide width is also contingent on ω. The widest waveguides, with critical radii ranging between ~60 and ≥100km from the vortex center coincide with low frequencies. Therefore the vortex core expands which is not as favorable for intensification. This effect is reflected in the decrease in RMW acceleration rates. It is important to note that the threshold to support VRW propagation without incurring radial wave trapping between two turning points is ~ 0.08V_{0}/r, resulting in continuous wave reflection within a very narrow radial interval, and excludes the critical radius.