A simple diagnostic model for the cross-channel distribution of the depth average velocity in curved open channels. Issue 2 (3rd April 2021)

• Record Type: Journal Article
• Authors: Russell, Peter; Vennell, Ross
• Is Part Of: Journal of the Royal Society of New Zealand. Volume 51:Issue 2(2021)
• Page Start: 242
• Page End: 271
• Publication Date: 2021-04-03
• Subjects: Open channel -- curved flow -- depth average velocity -- secondary circulation; Science -- Periodicals; 505
• DOI: 10.1080/03036758.2020.1803926
• Languages: English
• ISSNs: 0303-6758

Abstract

ABSTRACT: A simple diagnostic narrow channel shallow water model for the cross-channel distribution of the depth average velocity is developed. It is diagnostic, because the slope of the stream-wise free surface is specified and it models the cross-channel distribution of the depth average velocity without any knowledge of the velocity field. A non-dimensional parameter that encapsulates the channel dimensions and the relative importance of bottom friction to horizontal eddy viscosity is defined. Numerical solutions for the cross-channel distribution of the depth average velocity are obtained using values of this non-dimensional parameter for different cross-channel topographies. Numerical solutions for the depth average velocity are in turn used to find the cross-channel distribution for secondary flow and vertical velocity. Two-dimensional distributions of the vertical velocity in the n – z -plane show that changes in topography dominate the vertical velocity distribution. Three-dimensional tracers in a hypothetical open channel using scaling values from geophysical observations show that secondary circulation has a loose helical flow pattern of approximately one full rotation for every 360 ∘ 360 ∘ of curvature. It is not unreasonable to suggest that this 1:1 relationship describes the looseness of secondary circulation in geophysical data.