Observations on distorted turbulent wakes

Abstract

The question considered here is whether turbulent wakes can undergo a simple self-preserving development when convected through a duct of varying crosssection. A flow is described as self-preserving if the distributions of its mean-value properties at successive sections have the same basic shape, differing only in magnitude and lateral extent. In such flows the scales of the mean velocity variation and turbulence have been found to be proportional.

The wakes studied are concentrated near a plane of symmetry through a duct of changing rectangular section but constant area; the portion of the wake near the other plane of symmetry is considered. Measurements in the flows behind three circular cylinders reveal a lack of universality of the scales associated with self-preserving solutions of the momentum equation. The wakes of the smaller cylinders adopt the predicted form, but that of the largest does not. As it moves through the channel, this wake is compressed less rapidly by the imposed lateral strain than is predicted.

Interest is then concentrated on the equation governing the kinetic energy of the turbulence and in particular on the relative size of its two production terms, that representing the action of the mean wake shear and that representing the effect of the distortion applied by the duct. It is found that self-preserving wakes can form only in a few kinds of distorting convecting flow. In the experimental duct, which has exponentially varying walls, one of these is set up. Attention is concentrated on this case. A stability analysis (based on the criterion that a stable wake is one in which the total turbulence production decreases as a result of more rapid wake expansion) suggests that, when production by wake shear is greater than that by distortion, a stable self-preserving development is possible in which the turbulence scale and the velocity defect scale remain proportional. But in the alternative, distortion-dominated, case the velocity defect decreases continually relatively to the turbulence.

The experimental results are in accord with these predictions. The transition from shear-dominated to distortion-dominated wakes appears to take place when the production terms are about equal. The failure of the one experimental wake to adopt a simple self-preserving form can be attributed to the relatively slight organization of its turbulence when distortion is begun.