Planar hydraulic jump at small inclinations of a narrow rectangular conduit is investigated by means of extensive experiments and theoretical analysis. Both upslope and downslope flows are considered for “natural” jumps formed solely by viscous shear without any geometrical obstruction. The effect of increasing conduit tilt from $-ve$ (upslope) to $+ve$ (downslope) is similar to increasing liquid flow rate. Additional intricacies are noted when flow downstream of the jump approaches the conduit ceiling. In particular, upslope flow exhibits unique instabilities and undergoes a hysteretic excursion to regain the initial stable state. The hydrodynamic states observed for different flow rate and conduit inclination are consolidated as a phase diagram that identifies the natural jump regime bounded by supercritical flow, subcritical flow, and full bore flow throughout the conduit and also demonstrates the existence of multiple hydrodynamic states for a certain range of operating conditions. This study reports jump induced hysteretic flow in sloping conduits. Apart from experiments, the classical shallow water theory is reformulated by incorporating the effect of turbulent viscosity and lateral averaging along the conduit width to account for sidewall effects. Additionally, mass and momentum balance across the jump is used to identify the domain of the natural jump in horizontal conduits. The theoretical predictions are in close agreement with experimental results. This is an analysis of the turbulent natural jump in slightly deviated narrow conduits.

• Received 18 December 2020
• Accepted 14 July 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.084803