Spontaneous-adjustment emission of inertia-gravity waves by unsteady vortical motion in the hurricane core

It is well known that intense atmospheric vortices have the potential to spontaneously radiate inertia-gravity waves (IGWs) to the environment via frequency matching between the unsteady vortical motion and an intrinsic IGW. In the present work we undertake an analysis of a shallow water simulation of an actively radiating hurricane-like vortex to understand the nature of the emitted spiral waves, and to obtain insight into the ultimate implications of such radiation on the angular momentum and kinetic energy of the vortex. The initial condition is motivated by observations of hurricanes with elliptically-shaped eyewalls, and it consists of an offset vorticity monopole within an elliptically shaped vorticity ring. The simulated lifecycle proceeds in two phases. The first phase (lasting approximately 12 h) is marked primarily by inner-core vorticity rearrangement and mixing. The second phase (lasting more than 36 h) is marked by a prolonged episode of spontaneous adjustment emission of spiral IGWs to the environment. During the radiation phase, unsteady vortical motion in the core acts as an IGW source, constraining both the frequency and radial wavenumber of the emitted waves. The IGWs are sufficiently small amplitude that quasi-balance is preserved. The consequences of this are two-fold. First, the sustained outward radiation of IGWs to the environment does not significantly decrease the intensity of the mean vortex (only a 1.5% decrease in kinetic energy in 36 h, part of which is caused by frictional effects). Rather, vorticity mixing in the early phase is found to be much more significant. Secondly, the fuzziness of the slow manifold is found to be exponentially small because a balance (nondivergent) model using vorticity advection and inversion is sufficient for obtaining the important features of the vortical part of the flow. Based on these results, we hypothesize that intense hurricanes can sometimes enter into spontaneously radiative states, that the radiative aspects of these states are very difficult to observe, and that the emission of IGWs from their cores is often of little consequence for vortex intensification or decay. The validity of these idealized barotropic results needs to be tested using more complex baroclinic vortices and with the inclusion of moist processes.