In his now classical paper on pressure gradient turbulent boundary layers, Clauser concluded that equilibrium flows were very special flows difficult to achieve experimentally and that few flows were actually in equilibrium . However, using similarity analysis of the Navier–Stokes equations, Castillo and George  defined an equilibrium flow as one where the pressure parameter, was a constant. They further showed that most flows were in equilibrium and the exceptions were nonequilibrium flows where Λ≠constant. Using the equations of motion and similarity analysis, it will be shown that even nonequilibrium flows, as those over airfoils or with sudden changes on the external pressure gradient, are in equilibrium state, but only locally. Moreover, in the case of airfoils where the external pressure gradient changes from favorable to zero then to adverse, three distinctive regions are identified. Each region is given by a constant value of and each region remains in equilibrium with respectively.
Similarity Analysis for Nonequilibrium Turbulent Boundary Layers*
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division October 18, 2002; revised manuscript received March 15, 2004. Associate Editor: T. B. Gatski.
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Castillo , L., and Wang, X. (December 7, 2004). "Similarity Analysis for Nonequilibrium Turbulent Boundary Layers." ASME. J. Fluids Eng. September 2004; 126(5): 827–834. https://doi.org/10.1115/1.1789527
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