Measurement of the scaling of the dissipation at high Reynolds numbers

Abstract

We present experimental results from a mechanically driven turbulent flow in helium gas at low temperature. A large range of Reynolds numbers, extending over three decades (up to 5000 for ${\mathit{R}}_{\lambda }$) is investigated. We perform torque measurements and determine the dissipation locally by two methods, using the third-order structure function and the energy spectrum. Related quantities, such as the Kolmogorov and Taylor scales, are determined. Both methods give consistent measurements for ${\mathit{R}}_{\lambda }$>1000 but differences are observed at lower values. The scaling of the dissipation is determined by using a single power law to fit the whole range of Reynolds numbers; we recover the classical value (exponent equal to 3) when dissipation is calculated by using a third-order structure function, while a significantly lower value is obtained when a spectral method is used. The question of the viscosity dependence of the dissipation is thus left open. Several issues, such as the anisotropy, homogeneity of the flow, and Taylor hypothesis are discussed.