Hydraulic Flow through a Contraction: Multiple Steady States
Department of Mathematics, University of Wisconsin-Madison,
480 Lincoln Drive, WI 537061388, Madison, Wisconsin, U.S.A.
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 two-dimensional hydraulic jump in the contraction occur-
ring in a small section of the bc/b0 and Froude number parameter plane. Inviscid one-dimensional
hydraulic theory provides a comprehensive leading-order explanation, but quadratic friction is re-
quired to achieve quantitative agreement and stability.
PACS numbers: Valid PACS appear here
We consider shallow water flows through a contraction,
experimentally, analytically and numerically. This work