Internal gravity wave emission from a pancake vortex: An example of wave-vortex interaction in strongly stratified flows

At small Froude numbers the motion of a stably stratified fluid consists, of a quasisteady vortical component and a propagating wave component. The vortical component is organized into layers of horizontal motions with well-pronounced vertical vorticity and often takes the form of so-called "pancake" vortices. An analytical model of such a vortex that is a solution of the Euler-Boussinesq equations at a vanishing Froude number is constructed as a superposition of horizontal two-dimensional Kirchhoff elliptic vortices. This vortex is nonstationary and internal gravity waves are, therefore, excited by its motion. The radiation properties are studied by matching the vortex field with the far internal gravity wave field according to the procedure applied in acoustics to determine vortex sound. The structure of the gravity wave field is completely quantified. By calculating energy and angular momentum fluxes carried by outgoing waves and attributing them to the adiabatic change of the vortex parameters, we calculate the backreaction of the internal gravity waves radiation and show that, as in the case of acoustic radiation by the Kirchhoff vortex, this adiabatic evolution leads to an elongation of the vortex, and its eventual destabilization.