Lagrangian structure functions in turbulence: A quantitative comparison between experiment and direct numerical simulation

Abstract

A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. Experimental data, at Reynolds number ranging from $R_{\lambda }=350$ to $R_{\lambda }=815$ , are obtained in a swirling water flow between counter-rotating baffled disks. Direct numerical simulations (DNS) data, up to $R_{\lambda }=284$ , are obtained from a statistically homogeneous and isotropic turbulent flow. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. To this purpose, we discuss in detail the importance of statistical errors, anisotropy effects, and finite volume and filter effects, finite trajectory lengths. The local scaling properties of the Lagrangian velocity increments in the two data sets are in good quantitative agreement for all time lags, showing a degree of intermittency that changes if measured close to the Kolmogorov time scales or at larger time lags. This systematic study resolves apparent disagreement between observed experimental and numerical scaling properties.