 
Summary: APS/123QED
Hydraulic Flow through a Contraction: Multiple Steady States
Benjamin Akers
Department of Mathematics, University of WisconsinMadison,
480 Lincoln Drive, WI 537061388, Madison, Wisconsin, U.S.A.
Onno Bokhove
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands
(Dated: February 19, 2007)
We consider shallow water flows through a channel with a contraction by experimental and theo
retical means. The horizontal channel consists of a sluice gate and an upstream channel of constant
width b0 ending in a linear contraction of minimum width bc. 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 twodimensional hydraulic jump in the contraction occur
ring in a small section of the bc/b0 and Froude number parameter plane. Inviscid onedimensional
hydraulic theory provides a comprehensive leadingorder explanation, but quadratic friction is re
quired to achieve quantitative agreement and stability.
PACS numbers: Valid PACS appear here
I. INTRODUCTION
We consider shallow water flows through a contraction,
experimentally, analytically and numerically. This work
