Incompressible Mixing of a Shear Flow with Fluid at Rest

Abstract

The laminar and turbulent mixing of a nonuniform free stream with fluid at rest is investigated. Laminar and turbulent vorticity numbers are defined, which measure the relative importance of the free-stream vorticity as compared to the average vorticity present in the wake and which increase with the square root of x and with x, respectively. Solutions of the subject problem are given to a first approximation in the vorticity numbers. In comparing the characteristics of the mixing due to a nonuniform stream — UQ + uy with those due to the uniform stream u — UQ, it is found that vorticity effects over a given length are nearly always negligible in the laminar case but became sizable in the turbulent case. This is due to the usually higher rate of increase with x of the turbulent vorticity number. Results of the analysis, as applied to streams having constant vorticity over finite y length, indicate the practicability of the use of outer vorticity as a means to control the rate of transfer of properties between two different streams.