SYMMETRY METHODS IN TURBULENT BOUNDARY LAYER THEORY New wake region scaling laws and boundary layer growth M. Oberlack, G. Khujadze Fluid Mechanics Group, Technische Universit- at Darmstadt, Petersenstr. 13, 64287 Darmstadt, Germany oberlack@hyhy.tu-darmstadt.de, khujadze@hyhy.tu-darmstadt.de Abstract The Lie group or symmetry approach developed by Oberlack (see e.g. Ober- lack 2001 and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient (ZPG) turbulent boundary layer flow. In an extension of the earlier work a third scaling group was found in the two-point correlation (TPC) equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier-Stokes and Euler equations which respectively admits one and two scaling groups. The present focus is on the exponential law in the outer region of turbulent boundary layer and corresponding new scaling laws for one- and two-point correlation functions. Theoretical results are com- pared to direct numerical simulation (DNS) data of a flat plate turbulent bound- ary layer at ZPG and at two different Reynolds numbers Re θ = 750, 2240 with up to 140 million grid points. DNS data show good agreement with the theoret- ical results though due to the moderate Reynolds number for a limited range of applicability. Finally it is shown that the boundary layer growth is linear. Keywords: Lie group method, turbulent scaling law, wake law 1. Introduction The classical logarithmic law of the wall ¯ u + 1 = 1 κ ln(x + 2 )+ C. (1) is still considered as one of the corner stones of turbulence theory. In recent years there has been a variety of publications describing alternative functional forms of the mean velocity distribution in this region (Barenblatt, et al. 2000, George and Castillo 1997, Zagarola et al. 1997) some of which were rather controversial. Nevertheless, high quality data such as by ¨ Osterlund et al. (2000a), (2000b) show that the classical theory gives the most accurate de- in: IUTAM Symposium on One Hundred Years of Boundary Layer Research Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, August 12-14, 2004 Series: Solid Mechanics and Its Applications, Vol. 129 Meier, G.E.A.; Sreenivasan, K.R.; Heinemann, Hans-Joachim (Eds.) 2006, X, 494 p