Nonlinear Problems in Fluid Mechanics, Meteorology & Oceanography

Indiana University, Bloomington IN

Investigators

Abstract

Temam 0074334 The investigator and his colleagues study nonlinear problems from meteorology, oceanography, and fluid mechanics, using the mathematical tools offered by analysis, the theory of nonlinear partial differential equations, dynamical systems theory, and computation. The part of this project related to meteorology and oceanography focuses on the following areas: (1) Open boundary conditions for limited domain simulations and well posedness issues for meteorology and oceanography problems. (2) Balanced and unbalanced models in atmosphere sciences. (3) Well-posedness and stability problems in oceanography. The fluid mechanics topics focus on several aspects of turbulence theory, including the connection between the conventional theory of turbulence, the dynamical systems approach, and the Navier-Stokes equations. The investigators intend also to complete a research monograph on some of these aspects of turbulence. Central problems in meteorology and oceanography are concerned with understanding and predicting the behavior of the atmosphere and the ocean --- in what patterns do these fluids, air and water, move? The mathematical equations that describe the motions are difficult to analyze, and computations are also difficult because the physical phenomena are complex and nonlinear. In fluid mechanics, understanding fluid flows generally and turbulence in particular, and developing efficient numerical methods to compute these flows, are major themes. The investigators study several problems related to the behavior of atmosphere and ocean fluid flows and to their effective computation. They also study and develop computational methods for turbulent fluid flows of importance for industrial processes.