Nonlinear effects at propagation of long surface waves in the channels with a variable cross-section

Abstract

Analysis of the propagation of waves in the channels and straits of different geometry seems an important problem, since the change of the channel width, its depth and cross-sectional shape in general significantly affects the amplification and weakening of the spatial structure of the wave field. Propagation and deformation of single surface waves in the channels with a variable cross-section are analyzed within the framework of shallow-water equations. It is shown that nonlinearity is manifested in growth with time of the wave front slope steepness and its subsequent breaking. Height and length of a propagating wave are weakly influenced by nonlinearity. The distance traversed by a single wave up to its breaking decreases with growth of the wave height and diminution of its length. The wave amplitude characteristics are estimated depending on the channel depth and width. They are accurately described by the known Green’s law. The propagation of long waves in channels with different cross-sectional shape at the same maximum depth and width had been numerically analyzed. The strongest nonlinearity was detected in the channel with a triangular cross section, as in this case the cross-sectional area was the least with the same depth and width. The channel shape has no significant effect on the amplitude and wave characteristics.

Keywords

waves in fluid, waves of finite amplitude, wave propagation in channels, channel mathematical model, numerical solutions, manifestation of nonlinear effects.

DOI: 10.22449/1573-160X-2015-4-3-12

Download the article