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Center for Nonlinear Studies |
The statistical study of turbulence is usually performed by means of the structure functions. Whereas these quantities are very appropriate for the study of scaling laws, they do not give any information on the local topology of the flow, and hence on the dynamical quantities such as enstrophy or energy transfer, because they only give access to one of the eight independant components of the velocity gradient tensor. To avoid this inconvenient, M.Chertkov, A.Pumir and B.I.Shraiman have introduced a model which describes the dynamics of M, the whole velocity gradient tensor averaged on a volume whose characteristic scale lies in the inertial range. This model, which enables to compute the statistics of M as a function of scale, is formulated in terms of a set of stochastic differential equations. I will first present the solutions of this system that we have calculated in the semiclassical approximation, which is valid in the limit of small noises. The results of this approximation have enabled us to build a more precise method of resolution of the system. I will present the solutions of the model calculated with this method, and show their good agreement with experimental measurements.