Comparison of two-dimensional and three-dimensional models of wave rivulet flow over an inclined plane

The object of this study is a straight rivulet flowing over an inclined plate whose surface is covered with regular nonlinear waves. Such waves can be modeled in full three-dimensional statement, but it is also possible to use a simplified quasi-two-dimensional approach with self-similar shape of rivulet cross section. In this study we directly compare the results of two- and three-dimensional approaches to the shape of the wave rivulet surface reconstructed experimentally using the laser-induced fluorescence technique. It is shown that the three-dimensional model reproduces well the wave surface of a rivulet, including such three-dimensional peculiarities as the wave front curvature and minor perturbations of its rear slope. Though the two-dimensional model is unable to reproduce such peculiarities, it describes well the parameters and shape of a wave in the central longitudinal section of the rivulet.