The flow in weak turbulent hydraulic jumps

Abstract

Velocity and surface measurements in three turbulent hydraulic jumps are analysed in detail. The velocity measurements were obtained in a hydraulic ume using laser- Doppler velocimetry and the surface measurements were obtained using capacitance wave gauges. The purpose is to extract information about the flow field and the stresses in the jumps and the geometrical extension of the recirculating region called the roller. To achieve this we first ensure that the overall continuity and momentum conservation for the flow is satisfied. This includes comparison with the classical results for hydraulic jumps. It is found that deviations from uniform-depth Reynolds- averaged velocities and hydrostatic pressure give small but important corrections to the conservation equations. Careful evaluation of the velocity measurements in conjunction with the continuity equation makes it possible to determine the lower limit of the recirculating roller region. Measurements of the Reynolds stresses are analysed, in particular in the roller region, and a simple model established that illustrates the mechanisms of the flow in the roller and predicts well the stresses along the lower limits of the roller. In combination with the analysis of the vorticity distribution, this leads to a qualitative description of the processes for the generation of vorticity. It suggests both similarities and differences from the hypothesis of the existence of a shear layer inside the jump. Similarity profiles are developed for the variation of stresses, vorticity, and eddy viscosity along the lower limit of the roller. Finally, the total angular momentum for the jumps is examined and compared to the analysis of Hornung, Willert & Turner (1995).