Eulerian space–time correlations in turbulent shear flows

Abstract

This paper is concerned with the generic form of space–time correlations of instantaneous velocity fluctuations in turbulent shear flows. The study has as its basis the Kovasznay–Corrsin conjecture modified to account for inhomogeneities. Details of the modifications were dictated by comparison with direct numerical simulations of turbulent channel flow. For example, analysis of the simulations shows that the space–time correlations at optimal delay depict, when appropriately normalized, a form independent of turbulence component. It is also evident that the half width of the correlation grows, in the outer region of the layer, like Vn+1, while the Lagrangian time scale grows like Vn, where 2<n<3 and V is the mean convection velocity. The resulting generic form for the space–time correlation captures these effects well and brings to light a Reynolds number effect that is most evident in the tail of the correlations at nonoptimal delay.