Dissipative Scaling Functions in Navier-Stokes Turbulence: Experimental Tests

Abstract

A recent theoretical development in the understanding of the small-scale structure of Navier-Stokes turbulence has been the proposition that the scales $η_n(R)$ that separate inertial from viscous behavior of many-point correlation functions depend on the order $n$ and on the typical separations $R$ of points in the correlation. This is a proposal of fundamental significance in itself but it also has implications for the inertial range scaling behaviour of various correlation functions. This dependence has never been observed directly in laboratory experiments. In order to observe it, turbulence data which both display a well-developed scaling range with clean scaling behaviour and are well-resolved in the small scales to well within the viscous range is required. We have analysed the data of the experiments performed in the laboratory of P. Tabeling of Navier-Stokes turbulence in a helium cell with counter-rotating disks, and find that this data satisfies these criteria. We have been able to find strong evidence for the existence of the predicted scaling of the viscous scale.