Nonlocal eddy viscosity for Reynolds stress and passive vector flux in turbulence

Local eddy viscosity and diffusivity models are widely used to understand and predict turbulent flows. However, local approximations in space and time are not always valid for actual turbulent flows. Recently, a nonlocal expression for the turbulent scalar flux was verified using the direct numerical simulation (DNS) of homogeneous isotropic turbulence with an inhomogeneous mean scalar. A model for the nonlocal eddy diffusivity was proposed and validated using the DNS data. In this study, using a similar approach, a nonlocal expression for the Reynolds stress and the passive vector flux was investigated using the DNS of homogeneous isotropic turbulence with an inhomogeneous passive vector. The Green's function for the passive vector fluctuation was evaluated to obtain the nonlocal eddy viscosity. The nonlocal expression for the passive vector flux agreed with the value directly obtained from the DNS. The nonlocal effects accounted for the overestimation of the passive vector flux by the local expression as well as the phenomenon of the countergradient diffusion appearing in some regions. A model for the nonlocal eddy viscosity was proposed systematically in a customary manner in the statistical theory of turbulence. The nonlocal eddy viscosity obtained from the model agreed well with the DNS values, including its temporal behavior, and the nonlocal model reproduced the passive vector flux. Because it was already known that the nonlocal eddy viscosity for the passive vector flux can also be applied to the Reynolds stress, these results indicate that the nonlocal eddy viscosity model is useful for gaining insight into momentum transport in turbulence.