Flow Patterns, Roller Characteristics, and Air Entrainment in Weak Hydraulic Jumps: Does Size Matter?

A hydraulic jump is a stationary transition from an upstream supercritical to a downstream subcritical flow. Hydraulic jumps with relatively low Froude numbers may be observed downstream of low-head hydraulic structures and their flow properties have not been not well documented. In this study, the hydraulic properties were investigated experimentally in weak hydraulic jumps with an inflow Froude number Fr₁ = 2.1 and inflow depths 0.012 m < d₁ < 0.130 m. Three novel features of the study were (1) the very wide range of inflow length scales tested systematically, (2) the relatively high Reynolds number Re = 3.05 × 10⁵ achieved in the largest experiment, with the Reynolds number defined as Re = ρ × V₁ × d₁/μ, and (3) the broad range of inflow conditions. Although no air entrainment was observed at the lowest Reynolds numbers, some distinct air–water flow patterns were observed in the roller region, generally similar to those observed at higher Froude numbers. The ratio of downstream to upstream depths followed closely the analytical solution of the momentum principle irrespective of the inflow depth. On the other hand, noticeable scaling issues were observed in terms of the dimensionless roller length, length of air–water flow region, roller toe fluctuation frequency, and rate of air entrainment, with increasing dimensionless data with increasing inflow depths, hence Reynolds numbers. The present results have some practical implication in terms of physical modeling and upscaling of results for low-head hydraulic structures, including culverts and storm waterways, which typically operate with Reynolds numbers in excess of 10⁵.