Internal separated flows at large Reynolds number

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Abstract
Large-Reynolds-number analysis is given for separated flows that have the characteristic feature of being confined in the transverse direction. Two principal limits of the governing equation are obtained depending on whether the streamwise length scale is of order one or of the order of the Reynolds number. The corresponding two types of separated flows are discussed. A method of calculation is given for the second type of flow. It employs an expansion in the eigenfunctions of the Poiseuille flow development and the problem is reduced to solving nonlinear first-order ordinary differential equations that have a tendency to decouple rapidly. The method is tested by a detailed comparison of the results of the present calculation with finite-difference solutions of the Navier–Stokes equations for a channel with sudden expansion. Applicability to other configurations is illustrated by solving the problem of the flow in a channel with a base.