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Steady two-dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel

Jack S. Keeler

Benjamin J. Binder

Mark G. Blyth

  • School of Mathematics, University of Manchester, United Kingdom

  • School of Mathematical Sciences, University of Adelaide, South Australia, Australia

  • School of Mathematics, University of East Anglia, United Kingdom

  • *jack.keeler@manchester.ac.uk
  • †benjamin.binder@adelaide.edu.au
  • ‡mark.blyth@uea.ac.uk
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Phys. Rev. Fluids 3, 114804 – Published 26 November, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.114804

Abstract

Free-surface flow past a semi-infinite or a finite-length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalized hydraulic rise, and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite-length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite-length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic downstream.

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Phys. Rev. Fluids 3, 114804– Published 26 November, 2018
  • Received 13 June 2018
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