Abstract
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 ≈ $\mathit{\approx }$ 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 ≈ $\mathit{\approx }$ 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 $c\mathit{\ne }U$, 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.