J. Atmos. Sci., 65, 644-654.

On the wavelength of the Rossby waves radiated by tropical cyclones


Kyle D. Krouse
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY.

Adam H. Sobel and Lorenzo M. Polvani
Department of Applied Physics and Applied Mathematics and Department of Earth and Environmental Sciences, Columbia University, New York, NY.


Abstract

The authors present a theory for the zonal wavelength of tropical depression-type disturbances which occur as a result of Rossby wave radiation from a preexisting tropical cyclone. In some cases, such disturbances undergo tropical cyclogenesis, resulting in a pair of tropical cyclones; the theory then predicts the zonal separation distance of such tropical cyclone pairs.

Numerical simulations are presented in which a thermally forced vortex, superimposed on an initial state of rest, is moved at different velocities in a shallow water model on a sphere. Vortices moving westward generate coherent wave trains to the east or southeast (depending on the amplitude of the vortex) resembling those in observations. The zonal wavelengths of these wave trains in each case are well described by the linear stationary solution in the frame co-moving with the vortex. Vortices moving eastward or remaining stationary do not generate such wave trains. This is consistent with the linear theory, which admits no stationary solutions in such cases. The authors hypothesize that the wavelengths of observed disturbances are set by the properties of the relevant stationary solution. The environmental flow velocity which determines this wavelength is not the translation velocity of the tropical cyclone, but the difference between that of the TC steering flow and that of the steering flow of the radiated waves. The authors argue that this difference can be of the necessary magnitude and sign to generate the observed wavelengths if the environmental vertical shear is easterly, and if the tropical cyclone is steered by a mean flow that is deeper than the one steering the waves.