Spontaneous Emission of Internal Waves by a Radiative Instability

Abstract The spontaneous emission of internal waves (IWs) from balanced mesoscale eddies has been previously proposed to provide a source of oceanic IW kinetic energy (KE). This study examines the mechanisms leading to the spontaneous emission of the spiral-shaped IWs from an anticyclonic eddy with an order-one Rossby number, using a high-resolution numerical simulation of a flat-bottomed, wind-forced, reentrant channel flow configured to resemble the Antarctic Circumpolar Current. It is demonstrated that the IWs are spontaneously generated as a result of a loss of balance process that is concentrated at the eddy edge and then radiates radially outward. A 2D linear stability analysis of the eddy shows that the spontaneous emission arises from a radiative instability which involves an interaction between a vortex Rossby wave supported by the radial gradient of potential vorticity and an outgoing IW. This particular instability occurs when the perturbation frequency is superinertial. This finding is supported by a KE analysis of the unstable modes and the numerical solution, where it is shown that the horizontal shear production provides the source of the perturbation KE. Furthermore, the horizontal length scale and frequency of the most unstable mode from the stability analysis agree well with those of the spontaneously emitted IWs in the numerical solution. Significance Statement Spontaneous emission of internal waves (IWs) describes a process by which large-scale, slow oceanic currents can spontaneously emit IWs. Recent observations and numerical studies suggest that spontaneous IW emission can provide an important IW energy source. Identifying the mechanisms responsible for spontaneous IW emission is therefore of utmost importance because IW breaking has crucial effects on the oceanic large-scale circulation. This study examines the spontaneous emission of IWs from a numerically simulated anticyclonic eddy. We show that the emission process results from radiative instability when the perturbation frequency is larger than the Coriolis frequency. This instability mechanism can be significant across the oceans for flow structures with order-one Rossby numbers (a measure of flow nonlinearity).