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 s², enstrophy w², their respective production terms - s_ij s_jk s_ki and ω_iω_js_ij, and material derivatives, Ds^s/Dt and Dw²/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Re_λ = 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 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 ω² to the relatively shorter time scales of s² and ω_i ω_js_ij and -s_ijs_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 s² and 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 -s_ijs_jks_ki and s² and between -s_ijs_jks_ki and Ds²/Dt, in addition to a marked anti-correlation between ω_iω_js_ij and Ds²/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s² and its production term, -s_ijs_jks_ki.