Near‐separating, self‐similar turbulent boundary layer

Abstract

AbstractThe self‐similar flow in a turbulent boundary layer, which is in a state close to separation as a result of the effect of adverse pressure gradient, is investigated. Such a boundary layer has a triple‐deck asymptotic structure. Between outer and near‐wall regions above the logarithmic sublayer, i. e. the constant‐stress layer, an intermediate region — the gradient sublayer — is formed, where the shear stress varies linearly due to adverse longitudinal pressure gradient. In the external part of the gradient sublayer, the velocity profile obeys the square‐root law. The velocity profile obtained from the solution for the outer region satisfies a slip condition on the wall. The slip value decreases as the similarity parameter $\Omega = \sqrt{- \delta^* U'/U}$ increases and vanishes at the value of Ω = 0.0911, which corresponds to separation, here δ* is the displacement thickness, and U and U′ are the free‐stream velocity and its derivative with respect to the longitudinal coordinate. In this case, the exponent m in the law specifying the free‐stream self‐similar velocity distribution increases, with separation occurring not at the minimal value of m = −1/3, which corresponds to the strongest adverse pressure gradient, but at the value m = 0.228. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)