Numerical study of critical flow for seven types of weirs affected by dam-break like rapidly varied flow

Critical flow is defined under steady gradually varied flow conditions, yet its hydraulic characteristics remain unclear for unsteady rapidly varied flow in various overflow structures. This work investigates how the unsteady rapidly varied flow affects the hydraulic characteristics of the critical flow for seven types of weirs using the shallow water equations (SWE), the non-hydrostatic Serre-Green-Naghdi equations (SGNE), and the non-hydrostatic Reynolds-averaged Navier–Stokes equations (RANSE). Key findings include: (i) For flows with significant streamline curvature, the critical point is not generally located at the weir crest as predicted by steady gradually varied flow. Under steady flow conditions, the critical point deviates from the weir crest, indicating a significant influence of non-hydrostatic pressure. Under unsteady flow conditions, the critical point moves over time and differs from the critical point location of steady flow, demonstrating a significant impact of unsteadiness. However, the results from RANSE and SGNE show little discrepancy, indicating that the weak influence of non-uniform velocity. (ii) The hydrograph of unsteady critical flow shows better consistency between SGNE and RANSE. In contrast, the SWE generally deviates significantly from the SGNE and RANSE. Therefore, the optimal modeling choice is to use the SGNE or RANSE model. Steady rating curves apply to steady flow regions for small curvature structure using depth by RANSE, and for all structures using depth by SWE. (iii) The above conclusions are generally consistent for different overflow structures, indicating their universal applicability.