Incompatibility of the exponential scaling law for a zero pressure gradient boundary layer flow with Reynolds averaged turbulence models

Abstract

Analyzing the multipoint-correlation equations for parallel turbulent shear flows and zero pressure gradient turbulent boundary layer flows with the help of Lie symmetry methods, a new exponential scaling law has been derived in the work by Oberlack [“A unified approach for symmetries in plane parallel turbulent shear flows,” J. Fluid Mech. 427, 299 (2001)]. In the frame work of Lie group methods these solutions are called invariant solutions. From experiments [B. Lindgren, J. M. Österlund, and A. Johansson, “Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressuere-gradient turbulent boundary layers,” J. Fluid Mech. 502, 127 (2004)] and direct numerical simulations [G. Khujadze and M. Oberlack, “DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow,” Theor. Comput. Fluid Dyn. 18, 5 (2004)] the exponential velocity profile was clearly validated in the mid-wake region of high Reynolds number flat-plate boundary layers. It was identified as an explicit analytic form of the velocity defect law. Implementing the latter invariant solution into various Reynolds stress models it was found that none of the investigated models are in accordance with the exponential velocity law.