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APS/123-QED Hydraulic Flow through a Channel Contraction: Multiple Steady States

Summary: APS/123-QED
Hydraulic Flow through a Channel Contraction: Multiple Steady States
Benjamin Akers
Department of Mathematics, University of Wisconsin-Madison,
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 leading-order approximation, in which a
turbulent frictional parameterization 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


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering