Transient generation of spiral inertia-gravity waves from a geostrophic vortex

The emission of inertia-gravity waves (IGWs) from an exact geostrophic vortex in a rotating and stratified fluid is investigated by three-dimensional numerical modeling. An initially balanced geostrophic vortex inevitably generates IGWs with spiral patterns within a short transient time period through an instability mechanism. This result reinforces the nonexistence of exactly invariant slow manifolds. The direction of the rotation of spiral IGWs is clockwise for both anticyclonic and cyclonic geostrophic vortices, which is consistent with the theoretical prediction. Spiral patterning can be regarded as a universal feature of IGWs, which occurs in the transient generation process. In the vertical direction, the energy of IGWs is dominated by mode-1 in the generation and propagation processes, leading to weak dissipation and long-distance propagation. A comparison of barotropic and baroclinic vortices suggests that horizontal nonzero strain and vorticity are essential for the occurrence of this instability mechanism, while the presence of vortex baroclinicity increases the intensity of the IGWs. The amplitude of the IGWs increases linearly with the Rossby number in the range of 0.04-0.1. Additionally, the IGWs emitted from an anticyclonic vortex are stronger than those radiated from a cyclonic vortex. Anticyclonic and cyclonic geostrophic vortices transfer approximately 0.54% and 0.41% of their kinetic energy to IGWs in this transient generation process, respectively. This transient generation of IGWs can supply an energy pathway from mesoscale eddies to diapycnal mixing processes in the interior of the oceans.