Vortex Rossby Waves (VRWs) are intriguing physical phenomena whose significant role in Tropical Cyclone (TC) dynamics has gained wide acceptance. The earliest analyses hypothesized inward eddy fluxes of angular momentum carried by trailing spiral VRWs that propagate upstream relative to the TC's mean swirling flow. Development of the Asymmetric Balance theory set the stage for analysis of VRWs in a range of physical contexts. A key concept was axisymmetrization, in which the vorticity-conserving waves become increasingly filamented in a radially shearing mean flow and surrender their energy to the basic state. Increasingly realistic simulations of initially balanced Potential Vorticity (PV) perturbations support this idea; although unbalanced thermal perturbations are much less effective.Intellectual Merit:The VRW literature is, for the most part, conceptually difficult, even arcane, and reaching the frontier of knowledge is challenging. This project will support recasting much of the analysis in terms of numerical solutions in which the dynamic variables are Fourier transformed in azimuth and time with their radial (and often vertical) structure is computed using a tridiagonal solver. In this formulation, each Fourier component has fixed circumferential wavenumber and apparent frequency relative to the ground. Propagating VRW solutions are confined to an annular waveguide encompassing radii where the waves' Doppler shifted frequency lies between the Rossby wave cutoff frequency and zero.This approach is much simpler conceptually than piecewise continuous or WKB analytical solutions. Intermittently forced asymmetric VRW wavetrains are simulated by representing the forcing with a Fourier series in time. Paradoxically, the largest eddy angular momentum convergence in these calculations spans the locus of forcing even though most of the wave filamentation occurs near the Rossby wave critical radius tens of kilometers outside the eye. In general agreement with previous work, the simulated waves have inward and upstream phase propagation, but outward group propagation and inward eddy fluxes of angular momentum. This approach will be extended to baratropically unstable profiles and resonant instability of coupled VRWs and gravity waves. It will also be used to address the unresolved roles of standing VRWs and wave-wave interactions in idealized vortex motion studies.Broader Impacts: The project is designed to advance the science by reexamination and deepening understanding of the properties of vortex Rossby waves in the context of the numerical solutions and by making idealized simulations widely accessible. The new insights into convectively forced VRWs are an example. Extending this approach to unstable profiles, instability coupled with resonant gravity waves, and vortex motion promises to further elucidate these phenomena. Each of the studies is a manageable thesis topic for Florida International University graduate students. The conceptual simplicity of the numerical solutions will facilitate interpretation in terms of VRW concepts. All of the simulations will be coded as well documented MATLAB m-files and posted on the web with appropriate supporting documentation. Key outcomes will be publication journal articles, many with student first authors, and of an accessible review article as the project nears completion.
