Estimating discharge from undular hydraulic jumps: Feasibility assessment based on flume experiments
Rapids are common in steep rivers, often forming where flow transitions from supercritical (Froude number, Fr > 1) to subcritical ( Fr < 1) through a hydraulic jump. When upstream Fr is supercritical but close to 1, this transition may occur as an undular hydraulic jump, exhibiting a train of stationary waves downstream of the jump toe. Previous studies proposed a method to estimate discharge using only UHJ wave spacing and channel width combined with a wave dispersion equation for large water depths relative to the UHJ wavelength. This method is based on the hypotheses that, by their presence, UHJs indicate near-critical flow conditions ( Fr ≈ 1) and that wave celerity c is equal to and opposite the cross-sectionally averaged flow velocity U . However, these hypotheses have not been thoroughly tested. We used data from published UHJ flume experiments to test the hypotheses that Fr ≈ 1 and c = U , compare the deep-water and general wave dispersion equations, and evaluate the accuracy of discharge estimates. In these experiments, the stationary waves exhibited shallow depths relative to wavelength and flow was subcritical ( Fr < 1) when averaged across multiple wavelengths. Additionally, wave celerity more closely approximated the surface flow velocity than U . By using a Fr representative of actual conditions and applying a coefficient to correct for c ≠ U , the accuracy of the discharge estimates improved. This finding suggests that the critical flow-based method is robust and can produce reliable streamflow estimates if the remotely observed wave trains are correctly interpreted as UHJs, without requiring in situ measurements.