Abstract
The governing equation for steady two-dimensional channel flow are deduced from the equations of inviscid fluid dynamics. Streamline inclination and curvature effects are approximately accounted for. The integration procedure aims at the elimination of the spatially transverse coordinate; through it one arrives at a second order non-linear ordinary differential equation for the free surface profile having the form of an (extended) Bernoulli-equation and providing formulae for the pressure and velocity distributions. A second derivation, applicable to channels with horizontal Thalweg and arbitrary prismatic cross section, leads to a similar equation for the free surface profile. Illustrations concern solitary waves in rectangular and trapezoidal cross sections. Comparison of theoretical predictions of wave geometry with experiments indicate advantages of our formulation over previous more extensive ones.
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