Exact Mapping Of Nonlinear Turbulence To Linear Models: The Mechanism Of Anomalous Scaling
Itamar Procaccia, The Barbara and Morris L. Levinson Professorial Chair in Chemical Physics, The Weizmann Institute of Science, Rehovot, Israel
We propose a solution to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem.
The statistics of the auxiliary linear model are dominated by Statistically Preserved Structuresı which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. This solution is equally applicable for the scaling exponents of Navier-Stokes turbulence and for nonlinear shell models, demonstrating their anomaly and calculability.
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