Reynolds number and scale dependence of turbulent eddy decorrelation

Abstract

The temporal decay of the Lagrangian velocity correlation function of isotropic, homogeneous turbulence is calculated by following particle trajectories and via continued fraction representation. We report on the eddy size as well as on the Reynolds number dependence. Most remarkably, the exponential relaxation approximation for the correlation function turns out to be insufficient. Memory effects result in a considerable enhancement: the decay is more than an order of magnitude faster. The very high Reynolds number turbulent flow fields are generated by a reduced wave vector set approximation of the Navier-Stokes dynamics, but for smaller Re the conclusions are confirmed by direct numerical simulations. Two orders of magnitude of the Taylor-Reynolds number are covered, up to Reλ ˜ 104.