Unsteady Transcritical Flow Modelling Using Vertically-Averaged and Moment Equations

Transcritical flow occurs during the operation of hydraulic structures and in rivers. Understanding these flows is essential for the design of hydraulic structures and the risk evaluation of flooding. The transition across the critical depth occurs with significant streamline curvature effects, resulting in non-hydrostatic effects as typical in weir flow or undular bores. Hydraulic simulation is routinely conducted in industry by resorting to the de Saint-Venant (dSV) equations due to the reduced computational cost and relative accuracy of predictions from an engineering standpoint. However, non-hydrostatic flows as those occurring across the critical depth, are poorly predicted by the dSV equations. Suitable modeling tools for unsteady flow modelling of transcritical open channel flow are the Boussinesq-type equations; however, they often require the enhancement of the linear dispersion properties. An almost unexplored tool in this field is the so-called Vertically-Averaged and Moment (VAM) equations model. In this model extra degrees of freedom are introduced to model the non-uniform velocity components and non-hydrostatic fluid pressure. By using variational statements, moment equations are generated for the additional parameters. This work explores the capabilities of the VAM model as applied to (i) steady flows over an embankment weir, (ii) unsteady flows over a bottom sill, and (iii) dambreak flows with different up- to downstream water depth ratios. The VAM model results are compared with those obtained by the dSV and Serre-Green-Naghdi equations, thereby highlighting the accuracy of the VAM model to simulate transcritical flows.