Elowyn Yager
Carl J. Legleiter
Gordon Grant
Laura A. Hempel
Christina M. Leonard
Katherine Adler
Merritt Elizabeth Harlan
Becky Fasth
Daniel C. White
2026
<p><span>Rapids are common in steep rivers, often forming where flow transitions from supercritical (Froude number, </span><i>Fr</i><span> > 1) to subcritical (</span><i>Fr</i><span> < 1) through a hydraulic jump. When upstream </span><i>Fr</i><span> 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 (</span><i>Fr</i><span> ≈</span><span> 1) and that wave celerity </span><i>c</i><span> is equal to and opposite the cross-sectionally averaged flow velocity </span><i>U</i><span>. However, these hypotheses have not been thoroughly tested. We used data from published UHJ flume experiments to test the hypotheses that </span><i>Fr</i><span> ≈</span><span> 1 and </span><i>c</i><span> = </span><i>U</i><span>, 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 (</span><i>Fr</i><span> < 1) when averaged across multiple wavelengths. Additionally, wave celerity more closely approximated the surface flow velocity than </span><i>U</i><span>. By using a </span><i>Fr</i><span> representative of actual conditions and applying a coefficient to correct for <i>c</i> ≠ <i>U</i> </span><span>, 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.</span></p>
application/pdf
10.1029/2025WR040997
en
American Geophysical Union
Estimating discharge from undular hydraulic jumps: Feasibility assessment based on flume experiments
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