Non-linear wave interactions in rotating stratified fluid flow

In these pages we investigate a dynamical explanation for the origin and nature of the chevron-shaped IGWs which appear in the trough of the baroclinic mode in the Williams et al. [84] experiment. Our proposal is based on the asymptotic renormalization theory of Wirosoetisno, Shepherd, and Temam [93]. The procedure produces an O(epsilon) correction to the underlying quasi-geostrophic dynamics which has both a "slaved" term, which describes IGWs which are entirely dependent on the baroclinic mode and have no independent life of their own, and a "spontaneous generation" term, which contributes a freely propagating and rapidly oscillating component to the ageostrophic dynamics.;We compute the Wirosoetisno et al. slaved term and the spontaneous generation source term numerically and compare our results with the location, amplitude, and morphology of the IGWs observed in the laboratory. We also explore the rate at which the baroclinic mode leaks energy into the slaved, versus the spontaneously emitted, IGWs during the baroclinic cycle.;How do our numerically computed, O(epsilon) IGWs compare with those seen in the experiment? What percentage of the energy leaked from the vortical mode into the ageostrophic IGWs flows into the spontaneously emitted, versus the slaved, IGWs? Is there a reverse flow back into the vortical modes?;We find points of agreement, but no exact correspondence between the Wirosoetisno et al. correction terms and the generation mechanism of the IGWs observed in the laboratory. We also show that the influx of energy into the spontaneously emitted IGWs rises quadratically from zero to 4.92x10 -2 J/kg within the first 1.4 seconds of the baroclinic cycle, with very little (.03 percent) going to the slaved IGWs. Finally, we are able to show that this energy flux is one way---from the vortical modes into the ageostrophic modes. Combined with those of Peter Bartello [7], our energy results offer a strong indication that in a real fluid, spontaneously emitted IGWs are an extremely efficient way to transfer geostrophic energy to ageostrophic energy, ultimately to be dissipated by viscosity.