Prediction of Probability Functions for Fluid Systems

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This proposal is centered about development and exploitation of "mapping closure", a novel and powerful method for statistical modeling of the properties of turbulent flow fields. Mapping closure is based on the continuous distortion of fields with known statistics into approximations of flows developing according to known physical-dynamic laws. It has several advan- tages over traditional analytical approaches, particularly with regard to the prediction of the statistical properties of such fields, including entire probability distribution functions (pdf's). It can give meaningful estimates of improbable events, and since it can track structures in physical space it may lead to more realistic subgrid-scale representations. It is proposed that the method be applied to pdf's of 2-dimensional turbulence and of fields governed by quasi-geostrophic dynamics. The pro- posed work also encompasses the investigation of practical procedures for the calculations required; the publication of a pedagogically oriented paper to make the method's associated tools more widely available to the geosciences community; and the evaluation of its applicablity to subgrid representations. Although the first two applications of the method are of particular relevance to large-scale meteorology and oceanography, Kraichnan's work on the method has been closely followed by scientists in other disciplines. They have recognized that it can be applied to the large percentage of the fluid in the universe that is in turbulent motion in systems of all scales. These include those undergoing non-linear chemical reactions (as in combustion models), those used in mechanical engineering, and those considered in planetary science and in astrophysics.