Rossby wave radiation from non-translating and from moving vortices

We analyze the short-wavelength Rossby waves generated by a non-translating and by a moving vortex in an idealized environment. Using a fully nonlinear shallow water model on the sphere, a vortex is generated near the equator using a Gaussian mass sink. In the non-translating case, no significant stationary "wavetrain" response is observed. In the westward-moving case, a steady wavetrain response is observed to the southeast of the vortex. This structure is the result of Doppler-shifted short-wavelength Rossby waves radiated by the moving vortex. The characteristic horizontal length scale of the wavetrain varies with the translation speed.

This imposed westward movement is not meant to simulate the mean-flow by which the vortex is being steered -- it simulates the relative velocity between the flow relevant to the vortex and the flow that the Rossby waves propagate through. These flows can be different for such reasons as monsoon shear and the beta-gyre effect.

By varying this relative velocity it is possible, for reasonable values, to stretch the length-scale of this stationary structure to values observed during multiple cyclone events. This occurs due to the appearance of a new root in the equatorial dispersion relation when the Doppler-shifting effect is included (e.g. ~3000 km for a 5 m/s relative velocity between the flows). The stationary cyclonic anomaly thus generated has westward absolute phase propagation and is seen to grow in time as the energy propagation is eastward for these shortwave Rossby waves.

A linear analytic theory is developed to explain the wavelength of the structure and is compared with numerical results.