Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

摘要

AbstractWe study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔUw≡ 2Uw, pressure gradient dP/dxand viscosityν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocityuτ, andhis the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡Uwh/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized withuτandh; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear s