Conditions that Inhibit the Radiation of Inertia-Gravity Waves from a Cyclone

One important mechanism of inertia-gravity wave (IG wave) production in the atmosphere is latent heat release by moist updrafts. Another, connected to mountain waves, is topographic forcing. A third, more complex mechanism, is unforced radiation from jets and vortices. In this talk, we will reexamine a paradigm of the latter process. Specifically, we will consider spontaneous radiation of IG waves from a shallow-water cyclone on the f-plane, whose potential vorticity (PV) decreases monotonically with radius. The radiation is generated by a frequency matched vortex Rossby wave (VR wave) that lives in the core of the cyclone. We will present two necessary conditions for a VR wave, and its radiation field, to decay with time. The first condition is derived from linear theory, using a wave-activity formalism. It states that the radial PV gradient of the cyclone must exceed a certain threshold in the VR wave critical layer. This threshold increases with the intensity of radiation that the VR wave emits. The second condition is derived from nonlinear theory. It states that the initial amplitude of the VR wave must be sufficiently small, so that the VR wave mixes PV in its critical layer at a slower rate than γ. Here, γ is the decay rate of the VR wave, according to linear theory. Both conditions are quantitatively verified by numerical simulations. Time permitting, we will briefly address the analogous problem of internal IG wave radiation from a three-dimensional density-stratified cyclone, with and without moisture.