On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence

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Abstract
Kolmogorov postulated in 1962 [J. Fluid Mech. 13, 82 (1962)] that the magnitude of velocity increments δur across an inertial range distance r in high Reynolds number flows is typically (rεr)1/3, where εr is the locally averaged dissipation rate. This refined similarity hypothesis has been widely used in discussions of anomalous exponents of velocity structure functions in connection with the scaling exponents of εr. Recently Hosokawa and Yamamoto [Phys. Fluids A 4, 457 (1992)] have presented numerical evidence from turbulence simulations that δur is uncorrelated with εr in moderate Reynolds number flows. In the present paper, results of similar measurements are offered for flow fields with a wide range of Reynolds numbers obtained from high-resolution numerical simulations of both forced and decaying isotropic turbulence. The present results show clear evidence of correlations between δur and εr, irrespective of the Reynolds number. Kolmogorov’s hypothesis is verified for r somewhat larger than the viscous dissipation scale, but at much larger distances the correlation seems to be weaker.