Experiments on two-phase flow in hydraulic jump on pebbled rough bed: Part 1–Turbulence properties and particle chord time and length

This study reported and discussed turbulence characteristics, such as turbulence intensity, correlation time scales, and advective length scales. The characteristic air–water time scale, including the particle chord time and length and their probability density functions (PDFs), was investigated. The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length, whereas further downstream, the decay rate was higher. In addition, the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles. Triple decomposition analysis (TDA) was performed to determine the contributions of slow and fast turbulent components. The TDA results indicated that, regardless of bed type and inflow conditions, the sum of the band-pass ($T_u^{\prime }$) and high-pass ($T_u^{″}$) filtered turbulence intensities was equal to the turbulence intensity of the raw signal data (T_u). $T_u^{″}$ highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number. Additional TDA results were presented in terms of the interfacial velocity, auto- and cross-correlation time scales, and longitudinal advection length scale, with the effects of low- and high-frequency signal components on each highlighted parameter. The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream. The second part of this research focused on the basic properties of particle grouping and clustering.