Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

Abstract

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as $R{e}^4$, and not as $R{e}^3$ expected from Kolmogorov's theory, where $Re$ is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier-Stokes equations, and some problems of principle associated with existing LES models are highlighted.

18 pages

References in corpus (4)

• The multifractal nature of turbulent energy dissipation
• Exact Second-Order Structure-Function Relationships
• Local 4/5-Law and Energy Dissipation Anomaly in Turbulence
• Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

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