Nonlinear Problems in Fluid Mechanics, Meteorology & Oceanography

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Temam0074334 The investigator and his colleagues study nonlinear problemsfrom meteorology, oceanography, and fluid mechanics, using themathematical tools offered by analysis, the theory of nonlinearpartial differential equations, dynamical systems theory, andcomputation. The part of this project related to meteorology andoceanography focuses on the following areas: (1) Open boundaryconditions for limited domain simulations and well posednessissues for meteorology and oceanography problems. (2) Balancedand unbalanced models in atmosphere sciences. (3) Well-posednessand stability problems in oceanography. The fluid mechanicstopics focus on several aspects of turbulence theory, includingthe connection between the conventional theory of turbulence, thedynamical systems approach, and the Navier-Stokes equations. Theinvestigators intend also to complete a research monograph onsome of these aspects of turbulence. Central problems in meteorology and oceanography areconcerned with understanding and predicting the behavior of theatmosphere and the ocean --- in what patterns do these fluids,air and water, move? The mathematical equations that describethe motions are difficult to analyze, and computations are alsodifficult because the physical phenomena are complex andnonlinear. In fluid mechanics, understanding fluid flowsgenerally and turbulence in particular, and developing efficientnumerical methods to compute these flows, are major themes. Theinvestigators study several problems related to the behavior ofatmosphere and ocean fluid flows and to their effectivecomputation. They also study and develop computational methodsfor turbulent fluid flows of importance for industrial processes.