The Scaling of Lagrangian Structure Functions

We use stochastic closure theory to compute the structure functions of Lagrangian turbulence. These structure function exhibit Lagrangian scaling, without intermittency, for an initial time interval, but then pass over to a regime with Eulerian scaling, with intermittency, for larger times. Thus Lagrangian dispersion passes over to Eulerian dispersion. This pass over is controlled by the second structure function, by the Scaled Generalized Green-Kubo Relations. The ultimate time interval of decay seems to be controlled by the scaling of detached eddies, analogous to the scaling in the buffer layer of boundary layer turbulence. The dip observed in the log-derivatives of the structure function, with respect to the second structure function S2, is caused only by the time scales probed by S2. It seems better to take the log derivative with respect to t, instead of S2, to fully understand the different scaling regimes of Lagrangian turbulence.