Isotropic prestress theory for fully developed channel flows

The anisotropic distribution of turbulent kinetic energy in fully developed channel flows is examined by using an algebraic preclosure which relates the Reynolds stress to the mean field gradient and to a prestress correlation, ((I) double under bar + tau(R) del [(u) under bar])(T) . [(u) under bar' (u) under bar'] . ((I) double under bar + tau(R) del [(u) under bar]) = tau(R)[(f) under bar' (f) under bar']. Local fluctuations in the pressure field and in the instantaneous Reynolds stress are responsible for the prestress correlation tau(R)(2)[(f) under bar' (f) under bar']. Closure requires a phenomenological model for the anisotropic prestress 2k (H) double under bar, defined by 2k (H) double under bar = tau(R)(2)[(f) under bar' (f) under bar']-2 alpha (I) double under bar/3. The prestress coefficient alpha( = tau(R)(2)[(f) under bar' . (f) under bar']/2) depends algebraically on the components of the Reynolds stress, the mean velocity gradient, the relaxation time tau(R), and the turbulent kinetic energy k. Previously reported direct numerical simulations (DNS) results for fully developed channel flows (delta(+) = 395) are used to evaluate the behavior of the Reynolds stress for an isotropic prestress (IPS) correlation (i.e., (H) double under bar = (O) double under bar). The IPS theory predicts the existence of a nonzero primary normal stress difference and shows that a significant transfer of kinetic energy occurs from the transverse and normal components of the Reynolds stress to the longitudinal component for tau(R)parallel to del[(u) under bar]parallel to much greater than 1. The spatial distributions of the two nontrivial invariants of the anisotropic stress predicted by the IFS theory are consistent with DNS results for 10 less than or equal to y(+)less than or equal to 395. The practical utility of the isotropic prestress theory is further demonstrated by predicting the low-order statistical properties of the turbulence in the outer region of fully developed channel flows. Transport equations for the turbulent kinetic energy ansi the turbulent dissipation are used to estimate the spatial distributions of the turbulent time scales k/epsilon and tau(R). (C) 1999 American Institute of Physics. [S1070-6631(99)01005-3].