Application of extended self similarity in turbulence

Details Application of extended self similarity in turbulence Application of extended self similarity in turbulence

1997-04-11

arxiv.org/abs/chao-dyn/9704015v2

Nonlinear Sciences

Chaotic Dynamics

12 pages, 7 eps-figures, replaces version from April 11th, 1997; paper now in press at Phys. Rev. E

Scientific paper

10.1103/PhysRevE.56.5473

From Navier-Stokes turbulence numerical simulations we show that for the extended self similarity (ESS) method it is essential to take the third order structure function taken with the modulus and called $D_3^*(r)$, rather than the standard third order structure function $D_3(r)$ itself. If done so, we find ESS towards scales larger than roughly 10 eta, where eta is the Kolmogorov scale. If $D_3(r)$ is used, there is no ESS. We also analyze ESS within the Batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function. The Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds number of about 500.

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