Intellectual Merit: The project uses the effective energy method to comprehensively study symmetric instability in vortices and parallel shear flows with and without vertical shear. The work follows on previous successes in developing the effective energy method and applying it to establishing stability criteria for barotropic and Couette flows. As with these previous results, the work promises to provide stability criteria for baroclinic flows that can be applied more generally than using traditional normal modes methods. The project will address the interactions between stability, instability, and dissipative mechanisms such as double diffusion. The work will provide a theoretical basis for understanding the stability mechanisms that govern a range of oceanic and atmospheric flows.
Broader Impacts: The project addresses fundamental questions regarding the dynamics of geophysical flows, and is therefore relevant to understanding ocean currents and atmospheric winds. In particular, the work has potential broader impacts in advancing theoretical knowledge of shear flow and vortex stability in both the oceans and atmosphere. The work also has the potential to provide simple and unifying mathematical concepts to explain longstanding problems in geophysical fluid dynamics.
The Oceans and Atmosphere of Earth are full of currents and vortices, some very large, like hurricanes. These water and air flows sometimes undergo sudden changes. This is often called an `instability'. There are several types of instabilities and one of them is `inertial instability' also known as `symmetric instability' and even `centrifugal instability'. In the laboratory it is easily seen with simple experiments. A well-known example are the so-called `Taylor-Couette vortices' which are the result of the instability of a circular flow. It has been studied for many years, first mostly by meteorologists. It is thought to be the cause of for example `clear air turbulence' and other atmospheric phenomena. There are also numerous observations that this instability frequently occurs in the oceans. The purpose of this research was to predict what exactly happens and what we can expect to see afterwards. Generally a different flow forms after some time passes. In the NSF-sponsored research we discovered that we can predict very precisely what the new flows will be. This is remarkable because after the instability starts to develop, it is followed by a period of highly chaotic and turbulent fluid motions. But this reorganizes after a while and the chaos disappears. The new flow is found to be completely determined a priori by a conservation law, a law that says that the total `absolute momentum' is conserved. With this it is possible to calculate for example how much energy is lost during the instability.
