Anomalous scaling exponents in nonlinear models of turbulence.
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We construct, 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 structures" 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. The approach is equally applicable to shell models and to the Navier-Stokes equations.
Angheluta
Luiza
L
The Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, Israel.
Benzi
Roberto
R
Biferale
Luca
L
Procaccia
Itamar
I
Toschi
Federico
F