Vortex Rossby waves in cyclones in the tropical atmosphere are believed to play a role in the observed eyewall replacement cycle, a phenomenon in which concentric rings of intense rainbands develop outside the wall of the cyclone eye, strengthen and then contract inward to replace the original eyewall. In this paper, we present a two-dimensional configuration that represents the propagation of forced Rossby waves in a cyclonic vortex and use it to explore mechanisms by which critical layer interactions could contribute to the evolution of the secondary eyewall location. The equations studied include the nonlinear terms that describe wave-mean-flow interactions, as well as the terms arising from the latitudinal gradient of the Coriolis parameter. Asymptotic methods based on perturbation theory and weakly nonlinear analysis are used to obtain the solution as an expansion in powers of two small parameters that represent nonlinearity and the Coriolis effects. The asymptotic solutions obtained give us insight into the temporal evolution of the forced waves and their effects on the mean vortex. In particular, there is an inward displacement of the location of the critical radius with time which can be interpreted as part of the secondary eyewall cycle.

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Persistent URL dx.doi.org/10.1111/sapm.12095
Journal Studies in Applied Mathematics
Citation
Nikitina, L.V., & Campbell, L. (2015). Dynamics of Vortex Rossby Waves in Tropical Cyclones, Part 2: Nonlinear Time-Dependent Asymptotic Analysis on a β-Plane. Studies in Applied Mathematics, 135(4), 422–446. doi:10.1111/sapm.12095