Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Stochastic modeling in geophysics and atmospheric physics

Development of transport models in complicated heterogeneous structures, e.g., in porous media, is a challenging problem with reach applications in many environmental and industrial areas. The spatial, time, and other parameter scales vary so drastically that the conventional deterministic approaches are applicable only after a series of avergaing procedures. The resulting mean equations are not closed, but what is more important, the averaging procedures eliminate often the crucial properties, e.g., the superdiffusional transport. We develope two classes of stochastic models: (i) Eulerian stochastic models which are based on a random field simulation. The probabilistic structure of the flow is extracted from the measurements and analytic evaluations of PDE's with random coefficients. The (ii) Lagrangian stochastic models are constructed in the form of Langevin stochastic differential equations governing directly the dynamics of Lagrangian trajectories of tracers in the flow. Here the trick is to make consistent the statistical properties of the Eulerian and Lagrangian statistics. We suggest a series of both kinds of models and give some numerical illustrations.

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