Turbulent Lagrangian Velocity Statistics Conditioned on Extreme Values of Dissipation

Direct numerical simulation data for the Lagrangian velocity structure functions conditioned on the local (in time) rate of dissi- pation of turbulence kinetic energy are analyzed over a wide range of Reynolds numbers to seek direct evidence for Lagrangian Refined Similarity Hypothesis (RSH) scaling. The main focus is on testing the Refined Similarity predictions for the dependence on the local dissipation rate. In the dissipation sub-range there is clear evidence for RSH scaling at large values of the dissipation rate, but strong departures from RSH scaling at very small values. However, a detailed analysis of the dependence on Reynolds number of the results at small values of the local dissipation rate suggests a trend towards RSH scaling with increasing Reynolds number, but this can only be realized, if at all, for Taylor scale Reynolds numbers greater than 105. Within the inertial sub-range, there is limited evidence for RSH scaling, but again there is a trend towards more substantial scaling over a wider range of dis- sipation rates with increasing Reynolds number. The main conclusion is that RSH scaling may apply as an important theoretical constraint on the Lagrangian structure of turbulence in the large Reynolds number limit, but significant corrections to the theory exist at practical values of the Reynolds number.