Flow Patterns and Turbulent Kinetic Energy Budget of Undular Jumps in a Narrow Flume

This paper presents results obtained from a detailed analysis of the experimental data of three hydraulic jumps with low Froude numbers (1.5-1.9) in a narrow flume. With the increasing Froude number, the three generated jumps exhibit an initial increasing then decreasing undular behavior. The turbulent velocity fields are measured with a high spatial and temporal resolution using the particle image velocimetry (PIV) technique. Based on careful evaluations of the valid velocity vectors from the PIV measurements, it is possible to determine the free surface profile of the undular jump. The undular flow patterns are visualized by velocity redistribution between successive crests and troughs, which is further interpreted in terms of the pressure variation according to the curvatures of the undular streamlines. An examination of the momentum flux shows that the velocity and pressure contributions are basically comparable within the subcritical flow region, and the total momentum is generally constant throughout the entire jump except at the transition region immediately downstream of the jump toe. The distributions of the turbulent kinetic energy (TKE) and TKE budget terms are analyzed at characteristic longitudinal locations. The results reveal that the significant turbulent quantities, which are presumably related to the undular flow motion and surface oscillation, are mainly concentrated around the surface. The decomposed turbulent intensities present an anisotropic feature near the jump toe that gradually becomes isotropic with downstream diffusion. The detailed analysis of the isolated contributions of production, advection, diffusion, and dissipation provides new insights into the TKE budget balance around the undular free surface region, which may serve as a reference for future computational model studies.