A unified approach for symmetries in plane parallel turbulent shear flows

By Martin Oberlack. Journal of Fluid Mechanics, 2001

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High–Reynolds Number Wall Turbulence (2011, methodology): “Other extensions of the classic theory based on near asymptotics (Wosnik et al. 2000) and symmetry group methods (Oberlack 2001, Lindgren et al. 2004) result in a log law with a shifted origin, which is found to extend the fit to mean velocity data nearer to the wall (see also McKeon et al. 2005,…”
A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow (2008, background): “Wosnik, Castillo & George (2000) (see also Oberlack 2001) proposed that, inside the overlap region of 30 (1 − r)+ 0.1R+, the mean velocity profile is logarithmic with respect to (1 − r)+ + a+, where a+ is an offset parameter and is approximately −8 for pipe flow.”
Coherent structures in wall-bounded turbulence (2017, background): “A more rigorous presentation of this material is Oberlack (2001).”
Energy cascade and spatial fluxes in wall turbulence (2004, background): “…the classical form when homogeneous isotropic conditions are approached, while under uniform shear it reproduces the equation used for the scale-by-scale budget in homogeneous shear flow, Casciola et al. (2003) (see also Hinze 1959 and Oberlack 2001 for the derivation of closely related equations).”