Asymptotic analysis of plane turbulent Couette-Poiseuille flows

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Abstract
Matched asymptotic expansions, are used to describe turbulent Couette–Poiseuille flow (plane duct flow with a pressure gradient and a moving wall). A special modification of conventional eddy-diffusivity closure accounts for the experimentally observed non-coincidence of the locations of zero shear stress and maximum velocity. An asymptotic solution is presented which is valid as the Reynolds number tends to infinity for the whole family of Couette–Poiseuille flows (adverse, favourable, and zero pressure gradients in combination with a moving wall). It is shown that plane Poiseuille flow is a limiting case of Couette–Poiseuille flow. The solution agrees with experimental data for plane Couette flow, for the limiting plane Poiseuille flow, and for a special case having zero net flow and an adverse pressure gradient. The asymptotic analysis shows that conventional eddy diffusivity closures are inadequate for general Couette–Poiseuille flows.

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