“…observed in hydraulic jumps. Further supporting evidence for the positive correlation between Reynolds number and transfer efficiency includes: (1) The Reynolds number fromWilhelms et al (1981)'s data falls within the range of 1.4 × 10 5 to 1.6 × 10 5 , and the transfer efficiencies align more closely with our present study, surpassing the data fromZhao et al (2022); (2) Analyzing separately two groups of data fromKucukali and Cokgor (2020), one with a Froude number around 4, where an increase in Reynolds number from 7.6 × 10 4 to 1.9 × 10 5 , results in a transfer efficiency rise from 0.033 to 0.071, and another group with a Froude number around 5, showing an increase in Reynolds number from 9.5 × 10 4 to 1.7 × 10 5 leads to a transfer efficiency increase from 0.057 to 0.093.Wang & Chanson (2016) explored cases with Reynolds numbers between 2.1 × 10 4 and 1.6 × 10 5 , indicating roller surface dynamics and bubble dynamics are scale-sensitive.Particularly, as the Reynolds number increases, the frequency of roller surface oscillation tends to rise. Moreover, higher Reynolds numbers lead to enhanced turbulent shear forces, resulting in the breakup of larger bubbles, and a marked increase in the interfacial area.…”