Lagrangian time scales and its relationship to Eulerian equivalents in turbulent channel flow

Lagrangian and Eulerian time scales were obtained from the direct numerical simulation of turbulent channel flow at two Reynolds numbers based on the friction velocity and channel half-height,Reτ=80,100.The Lagrangian integral time scales and time microscales were compared to their Eulerian equivalents.It is found that the ratio of Lagrangian to Eulerian integral time scales is given by TiL/TiE=1+0.1y+ for y+≤10,and that the ratios between the Lagrangian to the Eulerian time microscales are almost the same irrespective of the components.Those increase with y+ are approximated by TiL/TiE≈ 2.75-1.75 exp "-yα+ ".These results also show that these expressions are independent of the Reynolds number.