SPH modeling of oscillating characteristics of hydraulic jumps

The oscillating characteristics and cyclic mechanisms in hydraulic jump are investigated and reproduced using a weakly-compressible XSPH scheme which includes both an algebraic mixing-length model and a twoequation turbulence model to represent turbulent stresses. The numerical model is applied to analyze oscillations of different jump types based on the laboratory experiments by Mossa (1999). Experimental investigations were carried out in the hydraulic laboratory of the Mediterranean Agronomic Institute of Valenzano (Bari) in a channel of 7.72 m long with a rectangular cross section of a width of 0.30 m and a height of 0.40 m. The comparison between SPH and experimental results shows an influence of different turbulence models, such as mixing length or Standard k-ε, on the amplitude spectrum and peak amplitude of the time-dependent surface elevation upstream and downstream of the jump. Numerical results show satisfactory agreement with measurements and most of the peculiar features of the flow are qualitatively and quantitatively reproduced. By analyzing a single cycle of the oscillating phenomena of a simulated jump (periodic formation of different jump types) it is possible to indicate the correlation between the vortex structures of the roller. Vortices are characterized by a clockwise or anti-clockwise rotation depending on which type of jump is present, particularly for configurations with alternations of wave and B jumps.