An Analytical and Experimental Study of the Plane, Incompressible, Turbulent Free-Shear Layer With Arbitrary Velocity Ratio and Pressure Gradient

A first-order approximation is derived in similarity coordinates for the velocity variation across a mixing zone between two streams of different velocities in an arbitrary pressure grudient. The velocity profiles obtained are functions of a single parameter, the ratio of the velocity of the slow stream to that of the fast stream. The first-order velocity profiles are compared to those obtained from the complete solution to the zero-pressure-gradient case obtained by Go¨rtler and good agreement is found when the velocity ratio is greater than 0.5. The form of the eddy diffusivity appropriate to the first-order theory is determined from analysis and experimental data. This form leads to an explicit transformation for the similarity coordinate requiring only a single empirical constant for all cases.