Vertically Averaged and Moment Equations Model for Flow over Curved Beds

Abstract

A new set of vertically averaged and moment equations, which assumes linear horizontal velocity distribution as well as quadratic vertical velocity and pressure distributions, along with a reduced set of vertically averaged equations similar to the Boussinesq equations, is investigated for flow over curved beds. Test results of measured and predicted water-surface and bed-pressure profiles for a horizontal to steep slope transition, symmetric and asymmetric bed profiles, and an idealized flip-bucket spillway are presented. The vertically averaged and moment equations perform satisfactorily for all three tests, while the reduced equations start to deviate from the measured results for large flows and in the cases of steep bed gradients and large bed and water surface curvatures. The satisfactory performance of the new set of equations is attributed to a higher degree of vertical detail incorporated in the model. The approaches presented are intended to extend the range of applicability of one-dimensional modeling to highly curved and steep flows.