On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

Abstract

We propose a new approach 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 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.

revised version with new data on Navier-Stokes eqs

References in corpus (1)

• Intermittency in Turbulence: computing the scaling exponents in shell models

Cited by in corpus (6)

• Lagrangian structure functions in fully-developed hydrodynamical turbulence
• The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges
• Computation of anomalous scaling exponents of turbulence from self-similar instanton dynamics
• Stochastic processes in turbulent transport
• Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results
• Perturbative anomalous exponents from Kolmogorov multipliers