Direct numerical simulation of strained three-dimensional wall-bounded flows

Abstract

Fully developed two-dimensional channel-flow turbulence is subjected to mean strains that imitate those produced by pressure gradients in three-dimensional boundary layers. This is achieved by applying irrotational temporal deformations to the flow domain in a conventional channel direct-numerical-simulation (DNS) code; straining deformations at an angle with respect to the initial flow direction generate a mean cross flow and thus mean three-dimensionality. The velocity difference carried by the near-wall region is further controlled by mean pressure gradients (or by accelerating the walls in-plane), thus introducing another effect of pressure gradients in boundary layers. “Numerical experiments” allow the effects of the inviscid skewing mechanism, adverse pressure gradient, and inner layer to be isolated; our primary interest here is in the outer layer. We present five simulations. In-plane skewing decreases both the Reynolds shear stress and turbulent kinetic energy, whereas strains characteristic of two-dimensional adverse pressure gradients increase them. In all cases, the structure parameter a1, the ratio of shear stress to energy, is diminished, which implies a reduction in the efficiency of the kinetic energy production by the mean shear.