An optimal shell model of turbulence

Abstract

We introduce a new shell model of turbulence which exhibits improved properties in comparison to the standard (and very popular) GOY model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular the second order correlation function is diagonal in the shell index, the third order correlation exists only between three consecutive shells. Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our choice of nonlinear coupling. We demonstrate that the model exhibits multi-scaling similarly to these GOY model. The scaling exponents are shown to be independent of the viscous mechanism as is expected for Navier-Stokes turbulence and other shell models. These properties of the new model make it optimal for further attempts to achieve understanding of multi-scaling in nonlinear dynamics.

accepted in PRE, revised version, REVTeX, 15 pages, 14 figures, included. Online (HTML) and PS versions of the paper available at http://lvov.weizmann.ac.il/onlinelist.html

References in corpus (4)

• Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling
• How the viscous subrange determines inertial range properties in turbulence shell models
• Cascades of energy and helicity in the GOY shell model of turbulence
• Universal scaling exponents in shell models of turbulence: Viscous effects are finite-size corrections to scaling

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