Approximate technique for calculation the celerity of long wave in channels with complex cross section

Abstract

Dynamic processes in rivers are always associated with long waves of a different type. The celerity of the waves is main property for calculating their propagation, and the shape of channels cross section is one of the factors affecting the celerity. Previously, the approach based on the principles of the theory of energy motion was used to study the dynamics of the waves. Several analytical solutions for the celerity were obtained for the channels with simple geometry of cross section such as rectangular, triangular, and trapezoidal ones. Developing the approach for similar calculations in natural channels, which cross sections have complex shape, the approximate technique is proposed in the paper. The technique needs information on the geometric properties of the stream and channel. Obtained solutions were compared with some field measurements of tidal bores in natural channels. Aim of the paper is to further develop the approach, which is based on principles of energy motion, to the analysis of unsteady fluid flow.