The Interaction of Convection & Internal Waves: A Natural Co-Dimension-Three Dynamics

Larry Redekopp, Hang Song
VIII th Int. Symp. on Stratified Flows   unpublished
The interactive dynamics involving convective motions in a layer heated from below and internal wave motions in a contiguous, stably stratified layer is analyzed in the weakly nonlinear limit. A reduced dynamical system consisting of three coupled, nonlinear amplitude equations describing the intensity of convection co-existing with bi-directionally propagating long internal waves is derived. This set is analyzed for various states of motion, and the results for special cases are discussed. In
more » ... are discussed. In particular, we identify critical conditions when both the long-wave mode and the shortwave mode become unstable, allowing a "resonant" coupling of unstable modes. The amplitude equation model also possesses a third-order phase dynamics which, at least in the weakly nonlinear limit, can describe episodic mixing events.