Laminar Boundary Layer Separation in a Uniform Shear Flow

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This paper describes theoretically the development and separation characteristics of a laminar boundary-layer flow over a flat plate placed in a uniform shear flow which is accompanied with a streamwise pressure gradient. The main flow is assumed as u'=U'(x')+wy' with U'(x')=U_0{1-(x'/l)^n}, where w, U_0 and n are constants. The govering equations have different forms in the leading edge region and in the vicinity of the separation point; the former is solved by the perturbation method, and the latter by the finite-difference method. The result shows that the separation of the boundary layer is affected considerably by the existence of w. It delays when w is positive, while it proceeds upstream when w is negative. The point of separatioin can be expressed as an expotential function of α=KR^<-1/2> for small values of α, where K=wl/U_0,R=U_0l/v and v kinematic viscosity. The analysis also shows that the effect of the external vorticity on the separation becomes less significant as the pressure gradient becomes smaller.
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