Inertial instability has been widely studied in meteorology where it is considered a source of clear air turbulence, rain bands, squall lines and atmospheric gravity waves. It has received much less attention in oceanography probably because it is generally thought to occur only for anticyclonically (clockwise) sheared parallel flows or anticyclones of strengths not typically observed in the ocean. However, there are many observations of anticyclonic currents in the ocean that are marginally stable, and this suggests that inertial instability may be the primary mechanism by which anticyclonic shear and anticyclonic vortices are maintained at stable or marginally stable values.
The criterion for inertial instability is often quoted as Rossby number less than minus one, where a negative Rossby number implies anticyclonic flow However this criterion applies only to flows in homogeneous fluids like the mixed layer with no vertical shear In stratified flow that is vertically sheared as is commonly the case inertial instability can also occur with Rossby numbers between -1 and 0. Furthermore, even cyclonically sheared flows or cyclonic vortices for which Ro is greater than zero can be inertially unstable if the vertical shear is strong enough. It is also interesting that this instability can occur when the Richardson number is well above a quarter that is, in flows that are stable to the Kelvin Helmholtz instability, a controlling factor in oceanic flows. In other words, flows that are stable with regard to the well known Richardson number criterion can, in fact, be unstable because of inertial instability. It is therefore possible that inertial instability is frequently a controlling factor in oceanic flows without having been recognized as such. This renewal proposal will continue studies of inertial instability with the object of providing a fundamental basis for understanding the role that inertial instability plays in the worlds oceans. Under prior NSF funding, the investigators have performed a systematic numerical study of the effect of varying basic parameters on the inertial instability of idealized model vortices with no vertical shear and with weak vertical shear. In addition, the resulting analytical model, based on plane parallel horizontally sheared flow, is able to explain and predict much of the fundamental results of the numerical studies. From these investigations, there are now guidelines for exploring further. The previous studies will be extended to much more realistic models of oceanic vortices. Through a series of numerical simulations the effects of inertial instability will be studied in a variety of model vortices over a wide range of the essential parameters.
Intellectual Merit: By undertaking our investigation of inertial instability, we hope to improve our understanding of the role that inertial instability plays in stabilization and maintenance of oceanic currents and eddies.
Broader Impacts: As a broader impact, these studies should provide guidance for those attempting to develop parameterizations for ocean models and criteria for determining likely locations for intense internal wave generation and inertial instability. Because of the intrinsically small vertical scales of inertial instability, it is usually not resolved by ocean models. Thus, the simulated flows can become and stay inertially unstable. This unphysical behavior must be corrected to maintain currents in the models at physically realizable levels, but a proper parameterization of the effects of the instability can be obtained only through increased understanding. This collaborative research project will foster an international collaboration with professor Orlandi at the University of Rome and one of his graduate students.
