Entrainment and the structure of turbulent flow

Abstract

Although the entrainment of non-turbulent fluid into a turbulent flow occurs across sharply defined boundaries, its rate is not determined solely by the turbulent motion adjacent to the interface but depends on overall properties of the flow, in particular, on those that control the energy balance. In the first place, attention is directed to the many observations which show that the motion in many turbulent shear flows has a structure closely resembling that produced by a rapid, finite, plane shearing of initially isotropic turbulence. The basic reasons for the similarity are the stability and permanence of turbulent eddies and the finite distortions undergone by fluid parcels in free turbulent flows. Next, the existence of eddy similarity and the condition of overall balance of energy are used to account for the variation of entrainment rates within groups of broadly similar flows, in particular mixing layers between streams of different velocities and wall jets on curved surfaces. For some flows which satisfy the ordinary conditions for self-preserving development, no entrainment rate is consistent with the energy balance and self-preserving development is not possible. Examples are the axisymmetric, small-deficit wake and the distorted wake. Finally, the implications of an entrainment rate controlled by the general motion are discussed. It is concluded that the relatively rapid entrainment in a plane wake depends on an active instability of the interface, not present in a constant-pressure boundary layer whose slow rate of entrainment is from ‘passive’ distortion of the bounding surface by eddies of the main turbulent motion. Available observations tend to support this conclusion.