Experimental analysis of scaling laws in low Re ^λgrid-generated turbulence

Abstract

An experimental investigation of scaling laws in turbulence generated by a biplane grid for low Reynolds numbers (Re ^λ) is presented. The present study covers a wide range of flow field conditions (from Re ^λ∼2.5 to Re ^λ∼36) that have not been analyzed from this point of view. It is shown that following the Kolmogorov theory a scaling range can not be observed since the separation between the energy production scales and the dissipative scales is too short. On the other hand, an extended form of scaling, the Extended Self-Similarity (ESS), permits the identification of a range of scales characterized by the same scaling exponent much wider than the one previously examined. Thus the scaling laws for the first six moments of the velocity structure function are accurately calculated by means of the ESS and an anomalous scaling with respect to the Kolmogorov theory is observed for Re ^λ down to the order of 10. As a matter of fact the scaling exponents are in good agreement with the ones that were determined at higher Re ^λ by previous experimental and numerical investigations. For Re ^λ≤6 a regularization of the scaling exponents is observed as an effect of the dissipation. We also present an analysis of the universality properties of the ESS form of scaling by means of the form function and an analysis of the sensitivity of the scaling range to the Re ^λ.