Physical Modelling, Scale Effects, and Self-Similarity of Stepped Spillway Flows

Stepped spillway flows are characterised by significant turbulent dissipation on the chute associated with strong free-surface aeration. Herein the validity of the Froude similitude is tested by re-analysing three experimental data sets corresponding to moderate slopes typical of embankment dams and storm waterways (θ = 3.4 to 22°). The measurements included distributions of void fraction, bubble count rate, interfacial velocity, turbulence intensity, bubble chord sizes, and integral turbulent length and time scales which were scaled with a 2:1 undistorted geometric scaling ratio. The criterion selection for scale effects is a critical issue. Major differences (i.e. scale effects) were observed in terms of bubble count rates, bubble chord sizes, turbulence levels and integral turbulent length scales although little scale effects were seen in terms of void fraction and velocity distributions. The findings suggested that most physical results, including the rate of energy dissipation and re-aeration, cannot be extrapolated to prototype flow conditions without significant scale effects. A complementary approach may be based upon self-similarity, since self-similar relationships were observed systematically at both macroscopic and microscopic levels.