On the non‐uniqueness of marginally separated boundary layer flows

A stationary or time dependent, laminar flow with a locally separated boundary layer is considered. The Navier‐Stokes equations are analysed with the method of matched asymptotic expansions. The resulting integro‐differential equation, known as the fundamental equation of marginal separation, is solved numerically by means of a spectral method based on Chebyshev polynomials. The critical value of the parameter controlling the magnitude of the adverse pressure gradient is associated with a bifurcation of the stability characteristics of the locally separated shear layer. The solution behaviour of the integro‐differential equation in the corresponding parameter space is investigated. Special emphasis is placed on the observed non‐uniqueness of solutions and the associated branch points.