Journal of Fluid Mechanics


Large-scale and very-large-scale motions in turbulent pipe flow

M. GUALA a1p1, S. E. HOMMEMA a1p2 and R. J. ADRIAN a1p3
a1 Laboratory for Turbulence and Complex Flow, Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA

Article author query
guala m   [Google Scholar] 
hommema se   [Google Scholar] 
adrian rj   [Google Scholar] 


In the outer region of fully developed turbulent pipe flow very large-scale motions reach wavelengths more than 8$R$–16$R$ long (where $R$ is the pipe radius), and large-scale motions with wavelengths of $2R$–$3R$ occur throughout the layer. The very-large-scale motions are energetic, typically containing half of the turbulent kinetic energy of the streamwise component, and they are unexpectedly active, typically containing more than half of the Reynolds shear stress. The spectra of the $y$-derivatives of the Reynolds shear stress show that the very-large-scale motions contribute about the same amount to the net Reynolds shear force, d$\overline{-u'v'}/{\rm d}y$, as the combination of all smaller motions, including the large-scale motions and the main turbulent motions. The main turbulent motions, defined as the motions small enough to be in a statistical equilibrium (and hence smaller than the large-scale motions) contribute relatively little to the Reynolds shear stress, but they constitute over half of the net Reynolds shear force.

(Published Online April 24 2006)
(Received July 7 2005)
(Revised December 21 2005)

p1 Present address: Institute for Hydromechanics and Water Res. Man., ETH Zurich, Switzerland.
p2 Present address: ExxonMobil Upstream Research Co., PO Box 2189, Houston, TX 77252, USA.
p3 Present address: Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287 USA.