Spreading and contraction at the boundaries of free turbulent flows

Abstract

The unstrained free turbulent flow generated by a composite grid has been found to possess a distinct, deeply indented boundary separating non-turbulent fluid from turbulent fluid of virtually homogeneous intensity. At this boundary, contraction, in the sense of a reduction in the volume of turbulent fluid, takes place at a rate which is independent not only of the intensity and degree of anisotropy of the turbulence, but also of the relative depth of the surface indentations. The apparent outward spreading of the turbulence is solely due to the increasing amplitude of the boundary bulges.

The subsequent plane straining of the flow in a constant area distortion shows that a reasonably high degree of anisotropy, combined with straining by the mean flow, is required before entrainment of non-turbulent fluid can occur at the boundary. Under these simple straining conditions, the rate of growth of the volume of turbulent fluid appears to be independent of the relative depth of indentations in the turbulence front.

It is considered that in free turbulent shear flows, the potential-turbulent flow boundary will advance into the non-turbulent fluid at a rate which depends on the local mean rate of strain and the local degree of anisotropy adjacent to the front. Contraction is expected to occur on those occasions when the boundary lies in a region of zero mean rate of strain, or when the anisotropy of the turbulence is low. The increased rate of spread due to large eddy activity is thought to be mainly caused by an increase in the probability of the potential-turbulent flow boundary being in a position where the mean rate of strain and local anisotropy are both high, rather than being entirely due to an increase in the surface area of the front.