Article ID: 2019-006
A simple conceptual model of the resonant interaction in a typhoon-like vortex between vortex Rossby waves (VRWs) and gravity waves (GWs), which are caused by the VRWs, is presented. It is well known that the VRWs in the central region of the vortex can grow by the interaction with the GWs in the outer region, but a simple conceptual model for their interaction has not yet been proposed. The proposed conceptual model is based on the buoyancy-vorticity formulation (BV-thinking), and is different from that for the barotropic and baroclinic instabilities based on PV interactions (PV- thinking).
We consider disturbances of the first baroclinic mode on a basic barotropic vortex. The disturbance vertical vorticity ζ of the VRW in the central region has a large amplitude on the upper and lower levels. While, the disturbance buoyancy b and radial vorticity η of the GW have a large amplitude on the middle level. The central VRW propagates (relative to the fluid) anticy-clonically, but moves cyclonically because of the strong cyclonic advection by the vortex. The outer cyclonically propagating GW is weakly advected also cyclonically by the vortex. As a result, the counter-propagating VRW and GW (satisfying Rayleigh's condition) may be phase-locked with each other (satisfying Fjørtoft's condition).
By the counter-propagation and phase-lock, the circulation around ζ of the VRW enhances b of the GW, which in turn enhances η. At the same time, the circulation around η of the GW enhances ζ of the VRW. As a result, the VRW and GW grow simultaneously.
We analytically show the possibility of the resonant interaction, and numerically obtain the growing solution in the system linearized about the basic vortex.