Nonlinearity tests of the Saint Venant equations

Mathias Foo, Erik Weyer

Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review


The Saint Venant equations are two nonlinear partial differential equations (PDE) which are used to describe the dynamics of one-dimensional flow in open water channels. Despite being nonlinear PDEs, the Saint Venant equations seem to exhibit linear behaviour in response to sinusoidal input signals. It is therefore of interest to determine "how nonlinear" the Saint Venant equations are. In this paper, we investigate the nonlinearity in the Saint Venant equations using several commonly used nonlinearity tests suggested in the literature. Five different open water channels are considered, and the results from the nonlinearity tests show that the Saint Venant equations are nearly linear in an operating region from at least half the nominal flow to twice the nominal flows, and many of the channels display linear behaviour in a larger operating region. This finding is useful as it further justifies the use of linear control design methodologies for open water channels. © 2013 IEEE.
Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)978-1-4673-5717-3, 978-1-4799-1381-7
ISBN (Print)978-1-4673-5714-2
Publication statusPublished - 10 Mar 2014
EventIEEE Conference on Decision and Control - Florence, Italy
Duration: 10 Dec 201313 Dec 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control


ConferenceIEEE Conference on Decision and Control


  • Equations
  • Correlation
  • Mathematical model
  • Harmonic analysis
  • Frequency response
  • Broadband communication
  • Time-domain analysis


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