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Updated: Jun 5, 2026

Simultaneous Measurement of Turbulence and Particle Kinematics Using Flow Imaging Techniques
Published on: March 12, 2019
Spectral theory of the turbulent mean-velocity profile
Gustavo Gioia1, Nicholas Guttenberg, Nigel Goldenfeld
1Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA.
Abstract:
It has long been surmised that the mean-velocity profile (MVP) of pipe flows is closely related to the spectrum of turbulent energy. Here we perform a spectral analysis to identify the eddies that dominate the production of shear stress via momentum transfer. This analysis allows us to express the MVP as a functional of the spectrum. Each part of the MVP relates to a specific spectral range: the buffer layer to the dissipative range, the log layer to the inertial range, and the wake to the energetic range. The parameters of the spectrum set the thickness of the viscous layer, the amplitude of the buffer layer, and the amplitude of the wake.
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