On the Wavelength of the Rossby Waves Radiated by Tropical Cyclones

Abstract

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 (TC). 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 experiments 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 comoving with the vortex. Vortices moving eastward or remaining stationary do not generate such trains, also consistent with linear theory, which admits no stationary solutions in such cases. It is hypothesized that the wavelengths of observed disturbances are set by the properties of the relevant stationary solution. The environmental flow velocity that determines this wavelength is not the translation velocity of the tropical cyclone, but the difference between the steering flow of the radiated Rossby waves and that of the TC. The authors argue that either horizontal or vertical shear in the environment of the TC can generate differences between these steering flows of the necessary magnitude and sign to generate the observed wavelengths.