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On the strength of the nonlinearity in isotropic turbulence

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In Navier-Stokes turbulence, the variance of the nonlinear term is smaller than it would be in a Gaussian random field with the same energy distribution. Analysis of the variance spectrum shows that this ‘depletion of nonlinearity’ is evidence of statistical dependence among the Fourier modes, even of modes corresponding to very large and very small scales. We apply the Direct Interaction Approximation to evaluate the scaling of the variance of the nonlinearity at high Reynolds number and show that it is dominated by sweeping effects. The variance reduces to its Gaussian value in thermal equilibrium; we show the growth and decay of the cumulant contribution to the variance of the nonlinearity in transient evolution of the spectrally truncated Euler equations from an assumed Gaussian initial state to a Gaussian final state of thermal equilibrium.

Author(s):

Robert Rubinstein    
United States

Wouter Bos    
CNRS - Ecole Centrale de Lyon
France