The flow of a laminar, incompressible jet along a parabola in the absence of an external stream is analyzed using the techniques of second-order boundary-layer theory. The first-order solution is the Glauert wall-jet solution. Second-order corrections in the jet due to the effects of curvature and displacement are obtained numerically after the external flow is corrected to account for the displacement effect. The shear stress at the wall is calculated and it appears that for values of the Reynolds number at which the governing equations are valid the jet does not separate from the parabola.
A new set of solutions to a singular second-order differential equation arising in boundary layer theory