Integral Turbulent Length and Time Scales in Hydraulic Jumps: an Experimental Investigation at Large Reynolds Numbers

A hydraulic jump is a rapidly-varied open channel flow characterised by the sudden transition from a supercritical flow motion to a subcritical regime. The transition is associated with a rapid increase of water depth, a highly turbulent flow with macro-scale vortices, significant kinetic energy dissipation, a two-phase flow region and some strong turbulence interactions with the free surface leading to splashes and droplet projection. The phenomenon is not a truly random turbulent process because of the existence of low-frequency, pseudo-periodic coherent structures and fluctuating motion in the jump roller. This study presents new measurements of turbulent air-water flow properties in hydraulic jumps, including turbulence intensity, longitudinal and transverse integral length and time scales, for a range of Froude numbers (3.8 < Fr1 < 8.5) at large Reynolds numbers (3×10 < Re < 2×10). The results showed a combination of both fast and slow turbulent components. The respective contributions of the fast and slow motions were quantified using a novel triple decomposition technique. The results highlighted the 'true' turbulent characteristics linked to the fast, microscopic velocity turbulence of hydraulic jumps, while showing that slow-fluctuation turbulence intensity was a significant contribution to the total. The high-frequency advection length scale and integral turbulent length scale exhibited some maxima in the lower shear flow next to the invert. The turbulent length scales decreased along the roller as the fast turbulence was dissipated. Comparison between the longitudinal advection and integral length scales indicated that the advection and diffusion were not independent processes in the flow region immediately downstream of the jump toe. The impact of slow fluctuations was large in the free-surface region and relatively smaller in the lower shear flow.