Numerical and analytical studies of geophysical flows and nonlinear waves

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My research spans a wide range of subjects, from theoretical fluid dynamics to numerical analysis. My primary research focus is on nonlinear interactions of waves in geophysical fluid flows, i.e., in the atmosphere and oceans. Wave interactions give rise to large-scale phenomena, such as the quasi-biennial oscillation between easterly and westerly winds that is observed in the tropical stratosphere, and smaller-scale phenomena, such as downslope windstorms and turbulence over mountains. It is important that wave effects are represented accurately weather and climate models. My investigations aim to provide us with the needed understanding of  the effects of the waves, as well as the mechanisms for their generation and propagation.One of my ongoing topics of interest is the development of parameterization schemes that are used in climate models to represent the drag force that results from gravity waves in the middle atmosphere. My other current interests in the field of geophysical fluid dynamics include the evolution of mountain waves in the lower levels of the atmosphere, planetary wave interactions in the atmosphere and ocean, and gravity wave propagation in the ionosphere, the region in the upper atmosphere where ions and electrons are present in large enough quantities to affect wave propagation.My secondary line of research involves numerical methods for solving partial differential equations. The methods that interest me are applicable to a variety of physical problems including, but not limited to, geophysical fluid dynamics. Recently I have studied high-order compact finite difference methods applied to problems which require numerical grids with non-uniform spacing, and alternating-direction explicit methods for modelling physical processes that include both fluid convection and heat diffusion. I am currently investigating the implementation of non-reflecting boundary conditions for use in fluid simulations.