Mechanisms for spontaneous gravity-wave generation within a dipole vortex

Previous simulations of dipole vortices propagating through rotating, stratified fluid have revealed small-scale inertia-gravity waves that are embedded within the dipole near its leading edge and are approximately stationary relative to the dipole (Snyder et al. 2007, Viudez 2008, Zhang et al. 2009). We investigate the mechanism by which these waves are generated, beginning from the observation that the dipole can be reasonably approximated by a balanced, quasigeostrophic (QG) solution. The deviations from the QG solution (including the waves) then satisfy linear equations that come from linearization of the governing equations about the QG dipole and are forced by the residual tendency of the QG dipole (that is, the difference between the time tendency of the QG solution and that of the full primitive equations initialized with the QG fields). The waves do not appear to be generated by an instability of the balanced dipole, as homogeneous solutions of the linear equations amplify little over the time scale for which the linear equations are valid. Linear solutions forced by the residual tendency capture the scale, location and pattern of the inertia-gravity waves, although they over-predict the wave amplitude by a factor of 2. There is thus strong evidence that the waves are generated as a forced, linear response to the balanced flow. We also discuss the relation to and differences from other theories for wave generation by balanced flows, including those of Lighthill and Ford et al.