MOMENT MODEL OF NONUNIFORM CHANNEL-BEND FLOW .1. FIXED-BEDS

Abstract

A nonuniform, fixed-boundary, channel-bend flow is formulated as two coupled sets of equations, each comprising two simultaneous equations, derived from the cross-section-integrated equations (in circular cylindrical coordinates) of conservation of flux of moment of momentum, and the depth-integrated momentum and continuity equations. Boundary shear stresses are related to the primary-flow shear stress and the primary and secondary velocities. The equations are solved numerically and the results found to be in satisfactory agreement with experimental data. The moment formulation elucidates the interplay among the secondary and primary flows, notably the observed flattening of primary velocity profiles, over-shoot of the secondary flow, radial redistribution of the depth-averaged primary velocity, and the secondary translational velocity. The erodible-bed case is treated in the companion paper.