Correlators of Velocity Differences and Energy Dissipation as an Element in the Subcritical Scenario for Non-Kolmogorov Scaling in Turbulence

Abstract

We discuss the theoretical implications of the experimental results for the cross correlations between velocity differences and dissipative fields which are reported in the companion (preceding) letter (Eumphys. Lett., 28 (1994) 635). The first implication is that 3d hydrodynamic turbulence has no conformal symmetry. Secondly, the experiment confirms the non-conformal scaling behaviour of such correlations as predicted by the analytical theory of the present authors. The results of the measurements lend support to the subcritical scenario that was suggested recently as an explanation of the non-Kolmogorov scaling of the structure functions in large but finite Reynolds number turbulence. The scaling properties of high-Reynolds-number (Re) turbulence are usually probed by examining the structure functions of velocity differences S, (R) and the correlation functions of the dissipation field K,,(R). The former are obtained from the longitudinal part of the velocity differences 6u(x + R, x) E (u(x + R) - u(x)) .R/R,