Seminar on Spectra & turbulent friction in 2- and 3-dimensional rough-pipe flows

Professor Gustavo Gioia 

Okinawa Institute of Science and Technology Graduate University, Japan

This seminar will be chaired by A/P Tran Anh Tuan

The friction factor f determines the cost of pumping oil through a pipeline, the drainage capacity of a river in flood, and other variables of engineering interest. The classical experiments of Nikuradse indicate that for turbulent flows in smooth-walled pipes, f depends only on the Reynolds number Re in good accord with the empirical relation, f∝Re(-1/4). For rough wall, f depends only on the roughness r in good accord with the empirical relation, f ∝ r^(1/3) (equivalent to the Manning formula). Here we will demonstrate experimentally that for flows of the same type but in two dimensions (2D), the corresponding empirical relations are f ∝ Re^(-1/2), for smooth wall, and f ∝ r, for rough wall. These results cannot be explained using the standard theory of friction but are consistent with an alternative theory in which f is linked to the turbulent spectrum via the spectral exponent α, which in turn is set by the dimensionality of the flow: in 3D, α = 5/3 and the theory predicts f ∝ Re^(-1/4) and f ∝ r^1/3; in 2D, α = 3 and the theory predicts f ∝ Re^(-1/2) and f ∝ r. We conclude that the standard theory is incomplete. This talk summarizes research carried out over more than 20 years. All are welcome to attend; all concepts will be introduced during the presentation.

Gustavo Gioia is a professor at the Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan. He was previously an assistant professor (2000-2006) and an associate professor (until 2011) at the College of Engineering, University of Illinois at Urbana-Champaign. He held postdoctoral positions at the University of Minnesota and at Rutgers University, and is a graduate of Brown University (PhD, solid mechanics), Northwestern University (MS, theoretical and applied mechanics), and the University of Buenos Aires (diploma, structural engineering).