Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

Details Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

2005-06-17

arxiv.org/abs/nlin/0506038v2

Nonlinear Sciences

Chaotic Dynamics

18 pages

Scientific paper

10.1007/s10955-005-8666-6

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 $Re^{4}$, and not as $Re^{3}$ 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.

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