Reply to discussion by A.N. Pinheiro and J.F. Melo on “Effect of jet aeration on hydrodynamic forces on plunge pool floors”Appears in the Canadian Journal of Civil Engineering, 35(5): 521-530.

The Authors would like to express their appreciation for all the research work developed by the discussers and by the interest and attention that they paid to the paper. Before addressing the interesting aspects raised by the Discussers, one clarification must be made. They refer that the Authors ‘‘obtained air concentrations close to the stagnation point of the developed jet at the pool floor of max. 30%’’, whereas, in fact, this value refers to the concentration C0 at the entrance section (impinging section) of the jet into the pool. No air concentration measurements were made close to the pool bottom. Nevertheless, the visual observations of the jet showed quite clearly that the air bubbles were much sparser close to bottom, as expected. The air concentration would certainly present values significantly lower than at the impinging section. When designing the facility, the Authors considered usual prototype dimensions and the Froude similarity law to establish its basic characteristics (pool depths, jet thicknesses, and jet velocities) and, in doing so, they were aware of the scale effects concerning air compressibility, bubbles size, penetration depth, rising velocities, and their obvious influence in the magnitude of air concentration near the bottom. The work developed by Manso (2006) and Manso et al. (2006), measuring the effect of jet velocity in the air concentration at the jet stagnation point and the wall jet region, is a significant contribution to enlarge our understanding of this phenomena and of the hydrodynamic pressures due to jet propagation in rock joints and fissures. However, the Authors’ interpretation of the air effect in the air–water jet diffusion is that, due to the presence of air along the penetrating path of the plunging jet, a stronger slowing down effect in the stream is felt comparing to the one observed in an equivalent water jet. Even if any of the initially entrained air does not reach the pool floor, there is velocity attenuation due to the presence of air bubbles. Other aspects that also support the higher energy dissipation in air–water jets comparatively to water jets are the higher turbulence intensities as well as the wider diffusion angles (Melo 2001). The results presented by the Discussers are based on jet velocities of absolute magnitude that are, no doubt, comparable to the ones observed in prototype spillways and outlets (6 to 25 m/s). The same does not apply to the tested water cushions depths (0.20 to 0.67 m) and jet diameter (0.07 m), which are typical of those used in laboratory experiments. In fact, prototype jet dimensions for the velocities tested by the Discussers would be of the order of 1 to 3 m thick and prototype water cushion depths would frequently be above 10 m. So, the work developed by the Discussers focused on the influence of the jet velocity, but in doing so, they had also to neglect other aspects as the ones mentioned above, thus implying scale effects existence. To evaluate how influent all the scale effects are, prototype measurements are clearly required. The technical difficulties and the inherent costs did not allow having such measurements until now. More difficult seems to be the study of the influence of air entrainment in the pressure field underneath the concrete slabs, because of the simulation of slabs draining system, if it exists, or of the more or less continuous joint systems existing between the slabs and the foundation. However, in previous research developed in the same facility, Melo (2001) and Melo et al. (2006) showed that when a continuous draining system exists for slabs separated by open joints or by closed joints with a joint failure underneath the stagnation line (for a rectangular jet), the influence of pressure fluctuation underneath the slabs is negligible, either for experiments with or without artificial jet aeration, where the pressure mean values are the ones to be considered in the slabs stability analysis. Once more, scale effects due to air– water flow were unavoidable, but no significant pressure fluctuations were noticed despite the presence of air bubbles inside the joint system or underneath the slabs.

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