Correlation decay of Lagrangian velocity differences in locally isotropic turbulence

Abstract

The dynamical correlation decay of eddies in fully developed turbulent flows is considered. Eddies of different sizesr are represented by Galilei invariant velocity differences of two fluid elements moving along with the flow, which start a distancer apart. The equal-time statistical properties of the flow are used as partly theoretical, partly experimental input. The method used is the continued fraction representation of the time evolution operator's resolvent. Neglecting memory effects we find the decay rate in the inertial subrange being determined by the ratio of the energy dissipation and the eddy fluctuation strength (represented by the static second order structure function). The decay rate for small eddies,r→0, tends to a Reynolds number dependent constant. The influence of intermittency on the dynamics via statics is evaluated. Inadequate experimental and theoretical information about higher order static structure functions renders an evaluation of the memory contribution impossible. Scaling arguments indicate decreasing relative importance of memory effects in the inertial subrange with increasingr.