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Zero and negative entrainment in turbulent shear flow

In certain accelerated flows the entrainment in the boundary layer, as normally defined, may be either zero or negative; on the other hand, there is no reason to suppose, on physical grounds, that the spread of mean or fluctuating vorticity should cease or become negative in such flows. This paradox is resolved in the present paper. It is also shown that in the equilibrium turbulent sink-flow boundary layer, where the entrainment as normally defined is zero, the reduced advection along streamlines in the outer part of the layer comes about mainly through increased dissipation: there is no reason to assume any radical change in the turbulence structure.