An approach to the dominant frequency of coherent structures in macroturbulent flows

The macroturbulent dissipation in hydraulic jumps is accompanied by pressure fluctuations that act on the component structures of the stilling basin (slabs and anchors, walls) and on the forced dissipation elements (chute blocks, baffle piers and end steps) and may exposed them to fatigue, vibrations and cavitation due to pressure pulses. The National Water Institute (Argentina) has developed extensive research on pressure fluctuations in macroturbulent flows, contributing to define the influence of fluctuating pressures on the design of hydraulic jump stilling basins.

Macroturbulent energy dissipation generates dynamic actions on the component slabs, which are exposed to small relative displacements and the kinetic energy can be partially transformed into additional sub-pressure. Dimensionless coefficients related to fluctuating forces and moments were obtained by means of instantaneous measurements on piezometric taps distributed on an area that represents different rectangular slabs. Free hydraulic jumps on horizontal stilling basins downstream of a vertical sluice gate were considered, with Froude numbers between 3 and 6.

The characteristics of the coherent structures of the hydraulic jump downstream of a bottom gate were contemplated, considering the longitudinal position along the stilling basin. The autocorrelation coefficients of fluctuating forces were analyzed for different sizes of slabs, determining the magnitude of the time scale of the turbulence and the peak frequency of main vortices at different positions along the bottom.

A first conclusion is that Strouhal numbers coincide with those determined through energy density spectra obtained from records of fluctuating pressures. In addition, the slabs are subjected to stresses whose frequency is approximately constant for values of dimensionless size of slabs less than a critical value, and invariant with a distance up to 70% of the length of the hydraulic jump, adopting a monotonically decreasing trend towards downstream. Finally, pressure wave celerities are somewhat higher than those determined for jumps formed downstream of spillways.