Vortex Rossby Waves in a Numerically Simulated Tropical Cyclone. Part I: Overall Structure, Potential Vorticity, and Kinetic Energy Budgets*

Abstract

The asymmetric structure in the inner core of a numerically simulated tropical cyclone is analyzed in this study. The simulated tropical cyclone is found to be highly asymmetric in the inner core. In the mid–lower troposphere, the asymmetry in the core is dominated by azimuthal wavenumber-1 and wavenumber-2 vortex Rossby waves. These waves propagate azimuthally upwind against the azimuthal mean cyclonic tangential flow around the eyewall, and thus have a much longer cyclonic rotation period (by a factor of 2) than the period of a parcel moving with the cyclonic mean tangential flow around the circumference. They also propagate outward against the boundary layer inflow of the azimuthal mean cyclone. The waves are only visible within a radius of about 60 km from the cyclone center. Beyond this distance, the radial gradient of potential vorticity (PV) of the azimuthal mean cyclone is too weak to support the vortex Rossby waves. Although the divergent motion remains strong, the geopotential height and wind fields of the vortex Rossby waves are quasi-balanced, with confluent cyclonic (divergent anticyclonic) flow collocated with low (high) perturbation geopotential height. The waves spiral cyclonically inward with maximum amplitudes near the radius of maximum wind (RMW) in the horizontal and tilt radially outward with height. The upward motion of the waves leads cyclonic vorticity in both azimuthal and radial directions by about one-quarter wavelength, implying that convective heating, which is coupled with low-level convergence and upward motion, is the driving force for the vortex Rossby waves. A PV budget shows that diabatic heating contributes greatly to both the azimuthal mean PV and perturbation PV budgets. The PV tendency associated with diabatic heating is largely balanced by the advective (both horizontal and vertical) flux divergence of the symmetric PV, respectively, due to the asymmetric flow (vortex beta term, similar to the planetary beta term in the large-scale vorticity equation) for the vortex Rossby waves, and due to the symmetric flow for the symmetric cyclone. The vortex Rossby waves transport cyclonic PV from the eyewall to the eye, thus mixing the PV between the eyewall and the eye and spinning up the tangential wind in the eye at the expense of weakening the tangential wind near the RMW. Moreover, the PV tendency due to nonlinear processes associated with the wavenumber-1 vortex Rossby waves is a significant PV source for the wavenumber-2 vortex Rossby waves, indicating a strong wave–wave interaction in the eyewall. An eddy kinetic energy budget indicates that within the RMW, the vortex Rossby waves receive their kinetic energy from the azimuthal mean cyclone through baroclinic conversion and flux divergence of eddy kinetic energy due to the azimuthal mean vortex. Under the eyewall and just outside the RMW in the mid–lower troposphere, the main source for eddy kinetic energy is the eddy potential energy conversion, which is related to the asymmetric diabatic heating associated with moist convection in the eyewall. An interesting finding is that, in both the barotropic and baroclinic conversions, terms related to the radial flow of the azimuthal mean vortex are dominant and contribute to the kinetic energy of the vortex Rossby waves. The horizontal shear of the azimuthal flow of the mean vortex damps eddy kinetic energy, stabilizing the vortex Rossby waves in the mid–lower troposphere. However, both barotropic and baroclinic conversions related to the tangential flow of the azimuthal mean vortex, together with the eddy potential energy conversion, are responsible for the development of asymmetry in the outflow layer.