Hydraulic flow through a channel contraction: multiple steady states

B. Akers, Onno Bokhove

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    We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upstream steady and moving bores/shocks, and oblique waves in the contraction, as single and multiple steady states, as well as a steady reservoir with a complex hydraulic jump in the contraction occurring in a small section of the $b_c/b_0$ and Froude number parameter plane. One-dimensional hydraulic theory provides a comprehensive leading-order approximation, in which a turbulent frictional parametrization is used to achieve quantitative agreement. An analytical and numerical analysis is given for two-dimensional supercritical shallow water flows. It shows that the one-dimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly well, even though the two-dimensional oblique hydraulic jump patterns can show large variations across the contraction channel.
    Original languageUndefined
    Article number10.1063/1.2909659
    Pages (from-to)056601
    Number of pages15
    JournalPhysics of fluids
    Issue numberWP 08-02
    Publication statusPublished - 2008


    • EWI-14889
    • IR-65305
    • METIS-255125

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