Closure to “Self-similarity and Reynolds number invariance in Froude modelling” by V. HELLER, J. Hydraulic Res. 55(3), 2017, 293–309

flow, notably how the flow interacts with a boundary, be it a bed of particles or the interface with an another fluid. The altered interaction, in turn, changes the flow field. The statistics associated with large-scale turbulence structures and their effects on entrainment and transport processes at boundaries require further investigation in hydraulic modelling and experiments. How altered spectra of turbulence-derived fluctuations in velocity and pressure interact with a deformable boundary and affect the resulting waveforms (on a sediment bed or at an air–water surface) raises interesting questions. For example, it is well known (e.g. Raudkivi, 1998) that, in turbulent flow, the hydrodynamic force on a boundary is a markedly fluctuating quantity that has significant implications for entrainment and movement of particles, and thereby bed wave development. The need for further investigation grows when the primary modelling criterion departs from Froude modelling, and instead focuses on an entrainment criterion, as is the case for modelling bed-particle or air entrainment. Departure from strict Froude modelling quickly raises an issue regarding exaggeration of vorticity in turbulence structures such as wake eddies. The Froude modelling situations the writer mentions (flows involving hydraulic structures and/or deformable boundaries) perhaps may slip outside the realm of the true self-similarity, but they are common modelling situations. Most hydraulic modelling of hydraulic structures at reduced scale uses Froude modelling and for practical reasons cannot resort to Reynold modelling to get the flow details right. Froude-based hydraulic modelling requires recognizing the inherent approximations involved, designing the model to yield the necessary information about the main process under scrutiny, and knowing how potential scale effects may impact that information. Heller’s interesting paper elevates the level of scientific discussion regarding similitude in hydraulic modelling and laboratory experimentation. The Discusser enjoyed reading the paper and is interested to learn Heller’s thoughts regarding the two points the Discusser mentions. References