Free Surface Length Scale Estimation in Hydraulic Jumps

In the context of recent work by Brocchini and Peregrine [J. Fluid Mech., 449, pp. 225–254 (2001a); 449, pp. 255–290 (2001b)] in this paper we aim to document free surface elevations and free surface length scales in hydraulic jumps with Froude numbers between 1.98 and 4.82. Although information on bubble size, frequency, and velocities in hydraulic jumps is available in the literature, there is not much data on the features of the free surface, or on mixing layer thickness. In the present case, measurements at the free surface have been realized with two “homemade” miniature resistive wire gauges made of two parallel $50μm$ diameter wires $1mm$ apart. These instruments were calibrated dynamically over a range of frequencies up to $20Hz$⁠. The present results extend the range of Froude numbers for which two-phase measurements in hydraulic jumps are available. In most respects, it confirms earlier results obtained with different experimental techniques. Length scales at the free surface are deduced from a cross-correlation analysis of wire gauge measurements, and are compared with similar data obtained from images of the surface.