Turbulent length–time scales distributions in hydraulic jumps

Abstract

Air–water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-sized facility using phase-detection intrusive probes. The void fraction measurements showed the presence of an advective diffusion shear layer where the air concentration vertical distributions were successfully compared with an analytical solution of the advective diffusion equation for air bubbles. In the air–water shear layer, a new empirical relationship between the maximum air concentration decay as a function of both the distance from the jump toe and the inflow Froude number was derived. Air–water turbulent time and length scales were deduced from auto- and cross-correlation analyses based on the method of Chanson (2007). The result provided some characteristic transverse time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The turbulence time scale data showed an increase with the relative elevation above the bed, as well as some decrease with increasing distance from the toe. The dimensionless integral turbulent length scale Lxz/d1was closely related to the inflow depth.