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arXiv · 1210.1327

Stability of the Couette-Poiseuille flow by the Reynolds-Orr energy equation

F. Lam
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Abstract

The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization problem for the Couette-Poiseuille flow. The minimum Reynolds number for every Couette-Poiseuille velocity profile has been computed and compared with those available in the literature. For fully three-dimensional disturbances, it is shown that the minimum Reynolds number is in general smaller than the corresponding two-dimensional counterpart for all the Couette-Poiseuille profiles except plane Couette flow.

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F. Lam. 2012-10-04. Stability of the Couette-Poiseuille flow by the Reynolds-Orr energy equation. https://arxiv.org/abs/1210.1327

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