Analytical model for lateral depth-averaged velocity distributions in curved channels

Abstract

The distribution of depth-averaged velocity is crucial to many engineering problems. This paper presents an analytical solution for the lateral depth-averaged velocity distribution in a 120° curved channel with asymmetric trapezoidal cross-sections in which the curved flow is not fully developed. The proposed analytical model was derived from the streamwise depth-integrated Reynolds-averaged Navier–Stokes equation, which considers the bed stress, Reynolds stress, secondary flow and local flow acceleration. In addition, practical boundary conditions are proposed to consider the trapezoidal cross-sections with linearly varying side beds and the flow separation at the inner bank near the bend entrance. The analytical solutions using the proposed model were found to be in good agreement with measured data. The main contributions of this study are the development of a conventional analytical model for sophisticated circumstances and the proposal of practical boundary conditions that consider flow separation.