Exact Solution for Asymmetric Turbulent Channel Flow with Applications in Ice-Covered Rivers

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.