Non-Hydrostatic Transitional Open-Channel Flows from a Supercritical to a Subcritical State

Abstract

In this study, a depth-averaged numerical model was employed to investigate the two-dimensional flow features of transitional open-channel flows from a supercritical to a subcritical state. Compared to a shallow-water model, the proposed model incorporates supplementary terms to account for the effects of non-uniform velocity and non-hydrostatic pressure distributions. The model equation was solved numerically by means of the Adams–Bashforth–Moulton scheme. A wide variety of transitional open-channel flow problems such as hydraulic jumps was considered for assessing the suitability of the numerical model. The results of the model for the free-surface profile, pressure distribution, and characteristics of the first wave of an undular jump were compared with the experimental data, and the agreement was found to be satisfactory. Despite the effects of the three-dimensional characteristics of the flow and the bulking of the flow caused by air entrainment, the model performed reasonably well with respect to the simulations of the mean flow characteristics of the curvilinear turbulent flow problems. Furthermore, the results of this investigation confirmed that the model is more suitable for analyzing near-critical turbulent flow problems without cross-channel shock waves.

Free-flow discharge characteristics of an overshot gate: A non-hydrostatic numerical modeling approach

“…It is known that a rapidly-varied transition typically involves a curvilinear flow with substantial vertical curvatures of the streamline that lead to a nonhydrostatic pressure and non-uniform velocity distributions. As noted by Fawer (1937), Montes and Chanson (1998), and Zerihun (2004, 2021a, a higher-order approximation for the vertical distribution of the streamline curvature parameters is necessary in order to accurately treat the complex transition from a hydrostatic to a non-hydrostatic flow regime. By relaxing the weakly-curved flow approximation, Zerihun (2017b) deduced a Boussinesq-type model from the depth-averaged energy equation.…”

“…For the case of flow with a discontinuous freesurface profile such as a hydraulic jump, a higherorder model based on the momentum principle (e.g. Steffler and Jin, 1993;Zerihun, 2017aZerihun, , 2021a) can be employed to analyze the flow problem without a prior knowledge of the energy dissipation rate. Equations ( 1a) and ( 4) will be employed here to analyze the free-flow discharge characteristics of a full-width overshot gate.…”