R. Lee Panetta

Research

I do research of three different types: numerical simulation, analysis of observational data, and mathematical study of certain partial differential equations. Most of this work is related in one way or another to my interest in large-scale coherent structures that occur in planetary atmospheres and oceans.

The two kinds of structure in which I am primarily interested are extra-tropical zonal jets and diagonal convection zones (like the South Pacific and South Atlantic Convergence Zones). Extra-tropical jets are a product of turbulent interactions of processes occurring at a number of scales, and I study them using quasi-geostrophic models of baroclinic turbulence and primitive equation models. Diagonal convection zones result from the interaction of organized tropical convection with extra-tropical jet streams, and I study such zones using both observational data and simple primitive equation models.

My research has connections with theories of climate modeling and theories of pattern formation in nonlinear systems. With models based on relatively simple equation systems, it is possible to make progress on versions of some important issues that have analogues in climate modeling. Numerical models are discrete dynamical systems based on systems of partial differential equations. I am particularly interested in the rigorous establishment of relations between the long-time behavior of the systems of PDEs and the long-time behavior of the discrete dynamical systems. Study of the structure formation process in simple baroclinic systems has led me into investigations of the properties of simpler pattern forming PDE's, in particular the Kuramoto-Sivashinsky equation.

In a separate line of research, numerical simulation of the scattering of electromagnetic radiation, I am studying the use of discontinuous Galerkin methods to extend what is technically feasible in the regime of large particle size. Progress in this area is important for the understanding of various optical phenomena in the atmosphere as well as for the formulation of parametrization schemes in climate models.

Education

Ph.D., Mathematics, University of Wisconsin, 1978