Free-surface undulation and velocity turbulence in shallow undular hydraulic jumps

Abstract

Undular hydraulic jumps and bores occur in coastal and estuarial regions at small approach Froude numbers and introduce non-uniform evolution of hydraulic properties in the flow direction, affecting the transport and deposition of sediment and other materials. This paper reports an experimental study of relatively wide undular hydraulic jumps generated in a 1.4-m-wide flume, characterized by inflow aspect ratio less than 0.06 and no lateral shockwave crossing at the first standing wave crest. General free-surface shape observations were conducted for a range of Froude numbers between 1.5 and 2.9 and Reynolds numbers between 2.5 × 104 and 1.2 × 105, while detailed free-surface and velocity measurements were performed at longitudinal and transverse cross-sections using acoustic displacement meters (ADMs) and an acoustic Doppler velocimeter (ADV), at five Froude numbers from 1.5 to 1.9. The results highlight complicated relationship of the three-dimensional free-surface characteristics with the variation of Froude number, which exhibits different features at the first two waves and at other sequent waves. The velocity data highlighted unique features of turbulent velocity redistribution at the first wave, including the distributions of turbulence intensity and Reynolds shear stresses. Particular focus on the formation of a “quiet water” zone below the upward-deflected mainstream flow was reported, with presence of instantaneous reversing velocities above the channel bed. The flow pattern analysis was facilitated with mean vorticity characterization. The results reflect that the evolution of undular hydraulic jump with increasing Froude number is a process of gradual turbulence localization towards the first standing wave, and the transition to a breaking hydraulic jump is achieved by the formation of a surface roller at the steepened jump front overwhelming the “resistance” of the bottom “quiet water” zone and forcing a change in the main flow path.