DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow

Abstract

The Lie group approach developed by Oberlack (see [1] and references therein) is used to derive new scaling laws for zero pressure gradient turbulent boundary layer flow. A direct numerical simulation (DNS) is performed for its verification. The approach unifies a large set of scaling laws (invariant solutions) for the mean velocity of stationary parallel turbulent shear flows and extends the work done by Oberlack. From the two-point correlation equations the knowledge of the symmetries allows us to rederive a broad variety of invariant solutions for turbulent flows: the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a turbulent Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of flat-plate boundary layers. The present focus is on the exponential law and corresponding new scaling laws for one- and two-point correlations.