The hydraulic jump in open channel

In an open channel, a hydraulic jump is the sudden transition from a supercritical torrential inflow into a subcritical fluvial motion. The transition region between torrential and fluvial flows is called the roller, which is typically characterised by strong turbulence, spray and splashing, free-surface aeration, and energy dissipation.
The flow within a hydraulic jump is extremely complicated, three-dimensional and multi-phase. The basic flow properties across the jump may be evaluated based upon momentum considerations applied in an integral form in first approximation. Following the original work of Jean-Baptiste Bélanger (Bélanger 1841), the momentum principle may be applied between the upstream and downstream ends of the control volume.
The application of the equation of conservation of momentum, i.e. momentum principle, along the x-direction states that the rate of change of momentum flux equals the sum of the forces applied to the control volume in the x-direction for a steady flow. In addition, the equation of conservation of mass, also called continuity equation, gives another fundamental equation linking the upstream and downstream flow properties.
The hydraulic jump is a seminal flow motion in open channel hydraulics, with many practical applications. In open channel flows, a hydraulic jump takes place when an upstream supercritical flow transforms into a subcritical open channel flow. The hydraulic jump is a very turbulent flow motion associated with intense energy dissipation and air entrainment.
A basic understanding of open channel hydraulic engineering is most relevant in many real-word applications related to water security and flood protection. These are discussed in a number of relevant UA-cam video movies in the same Playlist at:
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Fluid mechanics and hydraulics in Hubert Chanson UA-cam channel { / @hubert_chanson }
Fundamentals of open channel hydraulics [Playlist]
Environmental hydraulics of open channel flows [Playlist]
Advanced hydraulics of open channel flows [Playlist]
The Hydraulic jump: Hydraulic jumps in open channels { • The Hydraulic jump: Hy... }
The Hydraulic jump theory: (1) Smooth rectangular channel { • The Hydraulic jump the... }
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Acknowledgements
Professor Colin J. APELT
Dr Hang WANG
References
BÉLANGER, J.B. (1841). "Notes sur l'Hydraulique." ('Notes on Hydraulic Engineering.') Ecole Royale des Ponts et Chaussées, Paris, France, session 1841-1842, 223 pages (in French).
CHANSON, H. (2004). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9).
CHANSON, H. (2012). "Momentum Considerations in Hydraulic Jumps and Bores." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 138, No. 4, pp. 382-385 (DOI 10.1061/(ASCE)IR.1943-4774.0000409) (ISSN 0733-9437).
WANG, H., and CHANSON, H. (2015). "Experimental Study of Turbulent Fluctuations in Hydraulic Jumps." Journal of Hydraulic Engineering, ASCE, Vol. 141, No. 7, Paper 04015010, 10 pages (DOI: 10.1061/(ASCE)HY.1943-7900.0001010) (ISSN 0733-9429).