An algebraic preclosure theory for the Reynolds stress⟨u′u′⟩is developed based on asmoothing approximationwhich compares the space–time relaxation of a convective-diffusive Green’s function with the space–time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time&tgr;Rassociated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and, (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using anisotropicmodel for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and aneddyviscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that&tgr;RS∼1,whereSrepresents the mean shear rate. The Reynolds stress model and a set of recalibratedk−&egr;transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than20×⟨uz⟩(0)/S,a theoretical result consistent with experimental observations. ©1998 American Institute of Physics.