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Turbulence and the Wall Scaling of Momentum Transfer in 2D Pipes

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Nicholas Guttenberg, Physics, UIUC
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We present two dimensional turbulent pipe flow simulations to test a model by Gioia, et al of the momentum transfer between a turbulent flow and the walls of a rough pipe. In this model, the momentum transfer between the flow and wall depends on the energy spectrum of the turbulent flow at scales comparable with the scales of the viscous layer and the wall roughness. This model reproduces the scalings of the friction factor in three dimensional pipe flow observed in experiments by Nikuradze in 1933. As two dimensional flows support both an inverse cascade and enstrophy cascade (corresponding to different energy spectra), we can test the connection between the energy spectrum and friction factor of turbulent rough pipe flows.