IAHR Document Library

« Back to Library Homepage « Journal of Hydraulic Research 2018 Issue 3

Improvements of series convergence to the rotating-channel flow problem using hydraulic solutions for a parabolic passage

Author(s): Peter Lundberg; Janek Laanearu

Linked Author(s):

Keywords: Channel flow; hydraulic control; power series; singularities; vorticity

Abstract: This study deals with the perturbative solutions of the constant-potential-vorticity hydraulic problem, where the lowest-order solution corresponds to that for a non-rotating parabolic channel. The analytical structure of the series expansions and the corresponding numerical solutions are presented for flow through a horizontally constricted passage, and it is demonstrated how the series solution can be used to bridge the gap between non-rotating and rotating hydraulic models. It was found that the perturbative expansions converged close to the branch-point that corresponds to critical flow in rotating channel. This was not the case for the sub- and supercritical solution branches, where the perturbative series proved to diverge for discrete values of the expansion parameter, and hence one focus of the study is on improving the convergence here. The location and character of the dominant singularities affecting the series convergence were determined from analysis of the expansion coefficients using Domb–Sykes plots, where after the convergence was improved using Euler transformation rather than by direct Padé summation.


Year: 2018

Copyright © 2024 International Association for Hydro-Environment Engineering and Research. All rights reserved. | Terms and Conditions