Nonlinearity tests of the Saint Venant equations

Abstract

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.