Hydraulic flow through a channel contraction: multiple steady states

We consider 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 two-dimensional hydraulic jump in the contraction occurring in a small section of the $b_c/b_0$ and Froude number parameter plane. Inviscid one-dimensional hydraulic theory provides a comprehensive leading-order explanation, but quadratic friction is required to achieve quantitative agreement and stability.