 
Summary: APS/123QED
Hydraulic Flow through a Channel 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
Institute of Mechanics, Processes and Control Twente
(Dated: November 3, 2007)
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 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 complex hydraulic jump in the
contraction occurring in a small section of the bc/b0 and Froude number parameter plane. One
dimensional hydraulic theory provides a comprehensive leadingorder approximation, in which a
turbulent frictional parameterization is used to achieve quantitative agreement. An analytical and
numerical analysis is given for twodimensional supercritical shallow water flows. It shows that the
onedimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly
well, even though the twodimensional oblique hydraulic jump patterns can show large variations
