Exact Solution for Asymmetric Turbulent Channel Flow with Applications in Ice-Covered Rivers
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 10
Abstract
Asymmetric turbulent channel flow, such as ice-covered river flow, is a century-old problem but still unsolved in hydraulics and fluid mechanics. This study finds exact solutions for its eddy (or turbulent) viscosity and mean velocity distributions, which are independent of any assumption without any fit parameter. Specifically, it first applies Guo’s quartic eddy viscosity and complete log-law from high-Reynolds-number pipe flow to symmetric turbulent channel flow. It then formulates a functional equation, involving both bottom and top plane shear velocities, to govern the eddy viscosity distribution in asymmetric channel flow. The analytic solution for the eddy viscosity then leads to a velocity distribution solution that includes four components: bottom shear velocity effect, top plane shear velocity effect, symmetric interaction between both about a critical point, and antisymmetric interaction between both. The velocity distribution solution agrees well with field data and so is applicable in ice-covered rivers. Laboratory data also confirm the velocity distribution structure, but a turbulent mixing intensity parameter depends on the Reynolds number. Therefore, future laboratory tests should focus on high-Reynolds-number flow.
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Acknowledgments
This research was supported by the U.S. Federal Highway Administration Hydraulics R&D Program (Contract DTFH61-349 11-D-00010) through the Genex System to the University of Nebraska-Lincoln, the China Open Fund research programs at the State Key Lab of Hydraulic Engineering Simulation and Safety (Contract HESS-1604), Tianjin University, and at the State Key Lab of Hydraulics and Mountain River Engineering (Contract SKHL1511), Sichuan University. The authors also thank Prof. M. P. Schultz at the U.S. Naval Academy for providing the data in Figs. 2 and 3 for symmetric channel flow.
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©2017 American Society of Civil Engineers.
History
Received: Nov 29, 2016
Accepted: Apr 21, 2017
Published online: Jul 21, 2017
Published in print: Oct 1, 2017
Discussion open until: Dec 21, 2017
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