Integral space–time scales in turbulent wall flows

A direct numerical simulation of the Navier–Stokes equations is used to compute the space–time correlations of velocity fluctuations in a turbulent channel flow. By examining the autocorrelation R(ξ,τ) of the longitudinal wall shear-stress as a function of the streamwise and temporal separations, the effects of the limited extent of the computational domain when (artificial) periodic boundary conditions are used can be described and quantified. A time scale similar to the conventional integral scale but statistically related to the life time of the turbulent structures is computed from spatio-temporal data. The convection velocity, defined as the direction in the ξ,τ plane where the autocorrelations have their maximum at vanishingly small time delay, is computed as a function of the distance from the wall, and compared with the data available in the literature. Based on autocorrelations, the accuracy within which Taylor’s hypothesis is verified is quantitatively assessed. Last, the effect of the spatial discretization on the statistical characterization of wall turbulence is discussed.