Velocity autocorrelations of decaying isotropic homogeneous turbulence

Velocity autocorrelations and the mean-square displacements of fluid particles are obtained for decaying, isotropic homogeneous turbulence by numerical simulation of the flow field, using 1283 and 256’ grids, and tracking several tens of thousands of fluid particles, using a third-order interpolation scheme. A self-preserving Lagrangian velocity autocorrelation coefficient is found in terms of a dimensionless time variable s, defined by ds =dtlfJt), under the observation of a power-law energy decay and the assumption that rs(t> is proportional to the Lagrangian integral timescale 57&. This timescale is in turn assumed to be proportional to the length scale of the energy-containing eddies Ze-K3”/~ divided by the turbulent velocity u ’ , where K= & I2 is turbulent energy and E is the energy dissipation rate.