Abstract
We derive an equation satisfied by the dissipation rate correlation function, \(\left\langle {\varepsilon (\vec x + \vec r,t + \tau )\varepsilon (\vec x,t)} \right\rangle \) for the homogeneous, isotropic state of fully-developed turbulence from the the Navier–Stokes equation. In the equal time limit we show that the equation leads directly to two intermittency exponents μ 1=2−ζ 6 and μ 2=z″4−ζ 4, where the ζ's are exponents of velocity structure functions and z″4 is a dynamical exponent characterizing the fourth order structure function. We discuss the contributions of the pressure terms to the equation and the consequences of hyperscaling.
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Jayaprakash, C., Hayot, F. An Equation for the Dissipation Rate Correlation and Its Implications for the Intermittency Exponent μ in Turbulence. Journal of Statistical Physics 111, 371–386 (2003). https://doi.org/10.1023/A:1022269427387
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DOI: https://doi.org/10.1023/A:1022269427387