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

Lagrangian auto- and cross-correlation functions of the rate of strain s(2), enstrophy omega(2), their respective production terms -s(ij)s(jk)s(ki) and omega(i)omega(j)s(ij), and material derivatives, Ds(2)/Dt and D omega(2)/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Re-lambda = 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 omega and the rate of strain tensor s(ij), 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 omega(2) to the relatively shorter time scales of s2, omega(i)omega(j)s(ij) and -s(ij)s(jk)s(ki). 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 of s(2) and omega(2). 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 -s(ij)s(jk)s(ki) and s(2) and between -s(ij)s(jk)s(ki) and Ds(2)/Dt, in addition to a marked anti-correlation between w(i)omega(j)s(ij) and Ds(2)/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s(2) and its production term, -s(ij)s(jk)s(ki).