Mathematical Sciences: Nonlinear Phenomena in Fluid Dynamics and Related P.D.E.'s with Applications to Atmosphere/Ocean Science

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9625795 Majda The investigator continues research on the theory and applications of partial differential equations to problems in turbulence and atmosphere/ocean science. He uses a combination of physical modelling, asymptotic methods, stochastic techniques, rigorous mathematical theory, and large scale computing to yield new insight into physical phenomena. This project studies specific topics in two areas: 1) turbulent reaction diffusion equations, and 2) averaging over fast, random, and statistical waves in geophysical flows. The work in area 1 involves the development of new stochastic, asymptotic, and computational methods for studying scaling behavior in turbulent diffision and turbulent reaction diffusion equations where the velocity fields have many spatio-temporal scales. Potential applications to atmosphere/ocean science are described here, including tracer scale up in the mesoscale and turbulent mixing in marine cloud topped boundary layers. The work in area 2 involves four distinct topics regarding geophysical flows: A) averaging over fast gravity waves and the obstructions to balanced dynamics; B) statistical theories for large scale coherent structure and the Antarctic circumpolar current; C) baroclinic instability and geostrophic turbulence; D) parameterization of strong mesoscale convection events in the tropics. The research in topics C) and D) involves specific collaborations with atmosphere/ocean scientists at GFDL in Princeton and at NCAR in Boulder. Behaviors of the atmosphere and ocean are complex and not well understood. This project aims at a better understanding of atmosphere and ocean flows. Such an understanding could lead to improved predictions of weather, climate, and environmental phenomena.