My research focuses on the physics of submesoscale oceanic and atmospheric fluid flows. The submesoscales are the intermediate spatial scales that bridge the regime of large, energy-carrying motions such as currents or mesoscale eddies, and the isotropic turbulent regime at which energy is dissipated. Submesoscale motions include inertia-gravity waves, small-scale vortices and rotating/stratified turbulence. A good dynamical understanding of the submesoscale regime is crucial to a many different problems that range from being able to predict pollutant dispersal in regional models, to atmosphere/ocean weather prediction, and global climate change.
The governing equations are the Navier-Stokes (N-S) equations and one (or more) diffusion equation(s). Together, they constitute a set of nonlinear, coupled, three-dimensional partial differential equations. Techniques grounded in Fourier analysis have proven most useful for solving these equations. Asymptotic and perturbation methods provide guidance in the weakly nonlinear regime. Statistical methods are also invoked.