The production of turbulent stress in a shear flow by irrotational fluctuations

Abstract

This paper is a study of how external turbulence affects an initially turbulence-free region in which there is a mean-velocity gradient dU/dz. Rapid-distortion theory shows how external turbulence induces irrotational fluctuations in the sheared region, which interact with the shear to produce rotational velocity fluctuations and mean Reynolds stresses. These stresses extend into the sheared region over a distance of the order of the integral scale L∞. Since the actual front between the initial external turbulence and the shear flow is a randomly contorted surface, the turbulence of a fixed point near the front is intermittent. Intermittency is included in the present analysis by a simple statistical model.Experiments were done in a wind tunnel with the flow divided by a plate extending from upstream to x = 0. Above the plate, turbulence was produced by a grid. Below the plate a low turbulence shear was produced by wire screens. The wake of the plate (x > 0) decayed downstream.Turbulent shear stress was observed to grow from zero to significant values in the interaction region. The magnitude and extent of the observed stress agrees reasonably well with predictions. We conclude that turbulent stresses can be produced by irrotational fluctuations in a region of mean shear, and that this effect can be estimated using rapid-distortion theory.