An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

Abstract

Lagrangian auto- and cross-correlation functions of the rate of strains2, enstrophy ω2, their respective production terms −sijsjkskiand ωiωjsij, and material derivatives, Ds2/Dtand Dω2/Dtare estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence atReλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensorsij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2to the relatively shorter time scales ofs2, ωiωjsijand −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes ofs2and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkskiands2and between −sijsjkskiand Ds2/Dt, in addition to a marked anti-correlation between ωiωjsijand Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay ofs2and its production term, −sijsjkski.