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A Serre-Like Dispersive Wave Model for Prismatic, Arbitrary Cross-Section Channels

Author(s): Damien Violeau

Linked Author(s): Damien Violeau

Keywords: Dispersive waves; Channel waves; Serre equations; Favre waves; Variational method

Abstract: Favre waves are an example of weakly dispersive nonlinear waves in channels and rivers. These waves cannot be modeled using the Saint-Venant equations because of their dispersive character, but the Serre equations are appropriate for this purpose. However, they were written for channels with rectangular cross-sections (Serre, 1953a, b). Here we construct Serre-like equations for channels of arbitrary cross-section, and we highlight a family of travelling wave type solutions, including solitary waves. For channels with trapezoidal sections, we show that this model represents well the amplitude of the Favre leading wave as a function of the Froude number.


Year: 2023

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