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NEW SCALING LAWS IN ZPG TURBULENT BOUNDARY LAYER FLOW

George Khujadze
Universitat Siegen, Chair of Fluid Mechanics Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany & Abastumani Astrophysical Observatory Ilia State University, Tbilisi 0160, Georgia

Martin Oberlack
Chair of Fluid Dynamics, Dept. Mech. Eng., TU Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany; Center of Smart Interfaces, TU Darmstadt, Germany; GS Computational Engineering, TU Darmstadt, Germany

Abstract

Lie group or symmetry approach applied to turbulence as developed by Oberlack (see e.g. Oberlack (2001) and references therein) is used to derive new scaling laws for various statistical quantities of a zero pressure gradient (ZPG) turbulent boundary layer flow. From the two-point correlation (TPC) equations the knowledge of the symmetries allows us to derive a variety of invariant solutions (scaling laws) for turbulent flows, one of which is the new exponential mean velocity profile that is found in the mid-wake region of flatplate boundary layers. Further, a third scaling group was found in the TPC equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier-Stokes and Euler equations which has one and two scaling groups respectively.