# Hydraulic Jump: A Brief History and Research Challenges

^{*}

## Abstract

**:**

## 1. Introduction

_{1}was linked to the higher downstream depth d

_{2}with the following equation:

_{1}and V

_{2}are the upstream and down-stream velocity, respectively.

## 2. State of the Art

#### 2.1. Experimental Studies on the Internal Flow in Hydraulic Jumps

_{1}is the inflow Froude number, and ε is the dimensionless integrated shear force introduced by the author.

_{τ}is the integrated bed shear stress over the hydraulic jump length; $\gamma $ is the specific weight of water, and b

_{1}is the width of the stilling basin in upstream.

#### 2.2. Experimental Studies on the Turbulent Features of Hydraulic Jumps

#### 2.3. Experimental Studies on Oscillating Phenomena of Hydraulic Jumps

- oscillations of hydraulic jump types do not depend on whether the bottom is made of erodible or non-erodible material;
- a suitable time scale may be defined both for oscillations of the jump types and for fluctuations of the jump toes with a flat and outlined bottom;
- analysis of the oscillating phenomena indicates a correlation among the surface profile elevations, velocity components and pressure fluctuations;
- analysis of the oscillating phenomena indicates change configurations of the surface profile of a hydraulic jump, as a function of the air concentration present in the roller.

## 3. Research Challenges

#### 3.1. Numerical Methods with an Eulerian Approach

#### 3.2. Numerical Methods with a Lagrangian Approach

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bidone, G. Expériences sur la propagation des remous. In Memorie Della Reale Accademia delle Scienze di Torino; Natural History Museum Library: London, UK, 1820; Volume 30, pp. 195–292. [Google Scholar]
- Guglielmini, D. Della Natura de’ Fiumi; Nuova Edizione con le Annotazioni di Eustachio Manfredi: Bologna, Italy, 1739. [Google Scholar]
- Bélanger, J.B. Essai sur la Solution Numérique de Quelques Problèmes Relatifs au Mouvement Permanent des Eaux Courantes (‘Essay on the Numerical Solution of Some Problems relative to Steady Flow of Water’); Carilian-Goeury: Paris, France, 1828. [Google Scholar]
- Leutheusser, H.J.; Alemu, S. Flow separation under hydraulic jump. J. Hydraul. Res.
**1978**, 17, 193–206. [Google Scholar] [CrossRef] - Harleman, D.R.F. Discussion of “Turbulence characteristics of the hydraulic jump” by Rouse, H., Siao, T. T., & Nagaratnam, S. Trans. ASCE
**1959**, 124, 959–962. [Google Scholar] - Peterka, A.J. Hydraulic Design of Stilling Basins and Energy Dissipators; United States Department of the Interior: Washington, DC, USA, 1958. [Google Scholar]
- Rajaratnam, N. The Hydraulic Jump as a Wall Jet. J. Hydraul. Div.
**1965**, 91, 107–132. [Google Scholar] [CrossRef] - Leutheusser, H.J.; Kartha, V.C. Effects of inflow conditions on hydraulic jump. J. Hydraul. Div.
**1972**, 98, 1367–1385. [Google Scholar] [CrossRef] - Hager, W.H.; Bretz, N.V. Hydraulic jumps at positive and negative steps. J. Hydraul. Res.
**1986**, 24, 237–252. [Google Scholar] [CrossRef] - Hager, W.H.; Bremen, R. Classical hydraulic jump: Sequent depths. J. Hydraul. Res.
**1989**, 27, 565–585. [Google Scholar] [CrossRef] - Hager, W.H. History of the Hydraulic Jump, United States; Bureau of Reclamation, U.S. Department of the Interior, Bureau of Reclamation, Engineering and Research Center: Washington, DC, USA, 1990.
- Wu, S.; Rajaratnam, N. Free jumps, submerged jumps and wall jets. J. Hydraul. Res.
**1995**, 33, 197–212. [Google Scholar] [CrossRef] - Carollo, F.G.; Ferro, V.; Pampalone, V. New solution of classical hydraulic jump. J. Hydraul. Eng.
**2009**, 135, 527–531. [Google Scholar] [CrossRef] - Vischer, D.L.; Hager, W.H. Dam Hydraulics; John Wiley Sons: Chichester, UK, 1998. [Google Scholar]
- Hager, W.H. Energy Dissipators and Hydraulic Jump; Water Science and Technology Library; Springer Science & Business Media: Dordrecht, The Netherlands, 1992; Volume 8, ISBN 978-90-481-4106-7. [Google Scholar]
- Riegel, R.M.; Beebe, J.C. The Hydraulic Jump as a Means of Dissipating Energy; Technical Reports Part III; Miami Conservancy District: Dayton, OH, USA, 1917; pp. 60–111. [Google Scholar]
- Rehbock, T. Die Bekämpfung der Sohlen-Auskolkung bei Wehren durch Zahnschwellen. Schweiz. Bauzt.
**1926**, 87, 27–31. [Google Scholar] - Safranez, K. Wechselsprung und die Energievernichtung des Wassers. Bauingenieur
**1927**, 8, 898–905. (In German) [Google Scholar] - Bakhmeteff, B.A. Hydraulics of Open Channels, 1st ed.; McGraw-Hill: New York, NY, USA, 1932. [Google Scholar]
- Rouse, H. On the Use of Dimensionless Numbers. Civil Eng.
**1934**, 4, 563–568. [Google Scholar] - Bakhmeteff, B.A.; Matzke, A.E. The hydraulic jump in terms of dynamic similarity. ASCE Trans.
**1936**, 101, 630–680. [Google Scholar] - Rouse, H.; Siao, T.T.; Nagaratnam, S. Turbulence characteristics of the hydraulic jump. J. Hydraul. Div.
**1958**, 84, 1–30. [Google Scholar] - McCorquodale, J.A.; Khalifa, A. Internal flow in hydraulic jumps. J. Hydraul. Eng.
**1983**, 109, 684–701. [Google Scholar] [CrossRef] - Ehrenberger, I. Wasserbewegung in Steilen Rinnen (Susstennen). mit Besonderer Berucksichtigung der Selbstbeliiftung. Z. Osterr. Ing. Archit.
**1926**. No. 15/16 and 17/18 (In German) [Google Scholar] - Resch, F.J.; Leutheusser, H.J. Le ressaut hydraulique: Measure de turbulence dans la region diphasique. (The hydraulic jump: Turbulence measurements in the two-phase flow region). J. Houille Blanche
**1972**, 4, 279–293. (In French) [Google Scholar] [CrossRef][Green Version] - Resch, F.J.; Leutheusser, H.J.; Alemu, S. Bubbly two-phase flow in the hydraulic jump. J. Hydraul. Div.
**1974**, 84, 137–149. [Google Scholar] [CrossRef] - Roshko, A. Structure of turbulent shear flows: A new look. AIAA J.
**1976**, 14, 1349–1357. [Google Scholar] [CrossRef][Green Version] - Babb, A.F.; Aus, H.C. Measurements of Air in Flowing Water. J. Hydraul. Div.
**1981**, 107, 1615–1630. [Google Scholar] [CrossRef] - Hoyt, J.W.; Sellin, R.H.J. Hydraulic jump as “mixing layer”. J. Hydraul. Eng.
**1989**, 115, 1607–1613. [Google Scholar] [CrossRef] - Chanson, H.; Qiao, G.L. Air Bubble Entrainment and Gas Transfer at Hydraulic Jumps; Research Report No. CE149; Department of Civil Engineering, University of Queensland: Brisbane, QLD, Australia, 1994; p. 68. [Google Scholar]
- Chanson, H. Air Bubble Entrainment in Free-Surface Turbulent Flows; Experimental Investigations. Report CH46/95; Department of Civil Engineering, University of Queensland: Brisbane, QLD, Australia, 1995; p. 368. [Google Scholar]
- Chanson, H. Air entrainment in two-dimensional turbulent shear ows with partially developed in fow conditions. Int. J. Multiph. Flow
**1995**, 21, 1107–1121. [Google Scholar] [CrossRef][Green Version] - Chanson, H.; Brattberg, T. Experimental study of the air–water shear flow in a hydraulic jump. Int. J. Multiph. Flow
**2000**, 26, 583–607. [Google Scholar] [CrossRef][Green Version] - Mossa, M.; Tolve, U. Flow visualization in bubbly two-phase hydraulic jump. J. Fluids Eng.
**1998**, 120, 160–165. [Google Scholar] [CrossRef] - Gualtieri, C.; Chanson, H. Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump. Environ. Fluid Mech.
**2007**, 7, 217–238. [Google Scholar] [CrossRef][Green Version] - Gualtieri, C.; Chanson, H. Effect of Froude number on bubble clustering in a hydraulic jump. J. Hydraul. Res.
**2010**, 48, 504–508. [Google Scholar] [CrossRef][Green Version] - Gualtieri, C.; Chanson, H. Interparticle arrival time analysis of bubble distributions in a dropshaft and hydraulic jump. J. Hydraul. Res.
**2013**, 51, 253–264. [Google Scholar] [CrossRef][Green Version] - Chanson, H. Hydraulic Jumps: Turbulence and Air Bubble Entrainment. J. Houille Blanche
**2011**, 3, 5–16. [Google Scholar] [CrossRef][Green Version] - Kucukali, S.; Chanson, H. Turbulence Measurements in Hydraulic Jumps with Partially-Developed Inflow Conditions. Exp. Therm. Fluid Sci.
**2008**, 33, 41–53. [Google Scholar] [CrossRef][Green Version] - Murzyn, F.; Chanson, H. Experimental Investigation of Bubbly Flow and Turbulence in Hydraulic Jumps. Environ. Fluid Mech.
**2009**, 9, 143159. [Google Scholar] [CrossRef] - Chachereau, Y.; Chanson, H. Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers. Int. J. Multiph. Flow
**2011**, 37, 555–564. [Google Scholar] [CrossRef][Green Version] - Wang, H. Turbulence and Air Entrainment in Hydraulic Jumps. Ph.D. Thesis, School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia, 2014. [Google Scholar] [CrossRef][Green Version]
- Felder, S.; Chanson, H. Turbulence, Dynamic Similarity and Scale Effects in High-Velocity Free-Surface Flows above a Stepped Chute. Exp. Fluids
**2009**, 47, 1–18. [Google Scholar] [CrossRef][Green Version] - Long, D.; Rajaratnam, N.; Steffler, P.M.; Smy, P.R. Structure of flow in hydraulic jumps. J. Hydraul. Res.
**1991**, 29, 207–218. [Google Scholar] [CrossRef] - Ohtsu, I.; Yasuda, Y. Transition from supercritical to subcritical flow at an abrupt drop. J. Hydraul. Res.
**1991**, 29, 309–328. [Google Scholar] [CrossRef] - Habib, E.; Mossa, M.; Petrillo, A. Scour downstream of hydraulic jump. In Proceedings of the Modeling, Testing & Monitoring for Hydro Powerplants Conference, Budapest, Hungary, 11–13 July 1994; pp. 591–602. [Google Scholar]
- Abdel Ghafar, A.; Mossa, M.; Petrillo, A. Scour from flow downstream of a sluice gate after a horizontal apron. In Proceedings of the 6th International Symposium on River Sedimentation, New Delhi, India, 7–11 November 1995; pp. 1069–1088. [Google Scholar]
- Chanson, H.; Toombes, L. Supercritical flow at an abrupt drop: Flow patterns and aeration. Can. J. Civil Eng.
**1998**, 25, 956–966. [Google Scholar] [CrossRef] - Mossa, M. On the oscillating characteristics of hydraulic jumps. J. Hydraul. Res.
**1999**, 37, 541–558. [Google Scholar] [CrossRef] - Mossa, M.; Petrillo, A.; Chanson, H. Tailwater Level Effects on Flow Conditions at an Abrupt Drop. J. Hydraul. Res.
**2003**, 41, 39–51. [Google Scholar] [CrossRef][Green Version] - Mok, K.M.; Mossa, M. Discussion on: Relation of surface roller eddy formation and surface fluctuation in hydraulic jumps. J. Hydraul. Res.
**2004**, 42, 207–212. [Google Scholar] [CrossRef] - Mossa, M.; Petrillo, A.; Chanson, H.; Yausda, Y.; Takahashi, M.; Ohtsu, I. Discussion on Tailwater level effects on flow conditions at an abrupt drop. J. Hydraul. Res.
**2005**, 43, 217–224. [Google Scholar] [CrossRef][Green Version] - Wang, H.; Chanson, H. Experimental study of turbulent fluctuations in hydraulic jumps. J. Hydraul. Eng.
**2015**, 141, 04015010. [Google Scholar] [CrossRef][Green Version] - Chachereau, Y.; Chanson, H. Free-surface fluctuations and turbulence in hydraulic jumps. Exp. Therm. Fluid Sci.
**2011**, 35, 896–909. [Google Scholar] [CrossRef][Green Version] - Zhang, G.; Wang, H.; Chanson, H. Turbulence and aeration in hydraulic jumps: Free-surface fluctuation and integral turbulent scale measurements. Environ. Fluid Mech.
**2013**, 13, 189–204. [Google Scholar] [CrossRef] - Valero, D.; Viti, N.; Gualtieri, C. Numerical Simulation of Hydraulic Jumps. Part 1: Experimental Data for Modelling Performance Assessment. Water
**2018**, 11, 36. [Google Scholar] [CrossRef][Green Version] - Viti, N.; Valero, D.; Gualtieri, C. Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water
**2019**, 11, 28. [Google Scholar] [CrossRef][Green Version] - Long, D.; Steffler, P.M.; Rajaratnam, N. A numerical study of submerged hydraulic jumps. J. Hydraul. Res.
**1991**, 29, 293–308. [Google Scholar] [CrossRef] - Chippada, S.; Ramaswamy, B.; Wheeler, M.F. Numerical simulation of hydraulic jump. Int. J. Numer. Methods Eng.
**1994**, 37, 1381–1397. [Google Scholar] [CrossRef] - Qingchao, L.; Drewes, U. Turbulence characteristics in free and forced hydraulic jumps. J. Hydraul. Res.
**1994**, 32, 877–898. [Google Scholar] [CrossRef] - Cheng, X.; Chen, Y. Numerical simulation of hydraulic jumps on corrugated beds. J. Hydraul. Eng.
**2005**, 10, 52–57. [Google Scholar] - Souders, D.T.; Hirt, C.W. Modeling entrainment of air at turbulent free surfaces. In Proceedings of the World Water and Environmental Resources Congress 2004, Salt Lake City, UT, USA, 27 June–1 July 2004. [Google Scholar]
- Gonzlez, A.E.; Bombardelli, F.A. Two-phase-flow theoretical and numerical models for hydraulic jumps, including air entrainment. In Proceedings of the XXXI IAHR Congress 2005, Seoul, Korea, 11–16 September 2005. [Google Scholar]
- Ma, J.; Oberai, A.A.; Lahey, R.T., Jr.; Drew, D.A. Modeling air entrainment and transport in a hydraulic jump using two-fluid RANS and DES turbulence models. Heat Mass Transf.
**2011**, 47, 911–919. [Google Scholar] [CrossRef] - Witt, A.; Gulliver, J.; Shen, L. Simulating air entrainment and vortex dynamics in a hydraulic jump. Int. J. Multiph. Flow
**2015**, 72, 165–180. [Google Scholar] [CrossRef][Green Version] - Bayon, A.; Valero, D.; García-Bartual, R.; Vallés-Morán, F.J.; López-Jiménez, P.A. Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environ. Model. Softw.
**2016**, 80, 322–335. [Google Scholar] [CrossRef] - Wei, W.; Hong, Y.; Liu, Y. Numerical Simulation on Hydraulic Characteristics of Free Hydraulic Jump on Corrugated Beds of Stilling Basin. J. Syst. Simul.
**2017**, 29, 918–925. [Google Scholar] - Gingold, R.A.; Monaghan, J.J. Smoothed particle hydrodynamics: Theory and application to nonspherical stars. Monthly Not. R. Astron. Soc.
**1977**, 181, 375–389. [Google Scholar] [CrossRef] - Lucy, L. A numerical approach to the testing of fusion process. Astronom. J.
**1977**, 82, 1013–1024. [Google Scholar] [CrossRef] - De Padova, D.; Mossa, M. Multi-phase simulation of infected respiratory cloud transmission in air. AIP Adv.
**2021**, 11. [Google Scholar] [CrossRef] - Gomez-Gesteira, M.; Rogers, B.D.; Darlymple, R.A.; Crespo, A.J.C. State-of-the-art of classical SPH for free-surface flows. J. Hydraul. Res.
**2010**, 48, 6–27. [Google Scholar] [CrossRef] - De Padova, D.; Meftah, M.B.; De Serio, F.; Mossa, M.; Sibilla, S. Characteristics of breaking vorticity in spilling and plunging waves. Environ. Fluid Mech.
**2020**, 20, 233–260. [Google Scholar] [CrossRef] - López, D.; Marivela, R.; Garrote, L. Smoothed particle hydrodynamics model applied to hydraulic structures: A hydraulic jump test case. J. Hydraul. Res.
**2010**, 48, 142–158. [Google Scholar] [CrossRef] - Federico, I.; Marrone, S.; Colagrossi, A.; Aristodemo, F.; Antuono, M. Simulating 2D open channel flows through an SPH model. Eur. J. Mech. B/Fluids
**2012**, 34, 35–46. [Google Scholar] [CrossRef] - Jonsson, P.; Andreasson, P.; Gunnar, J.; Hellström, I.; Jonsén, P.; Staffan Lundström, T. Smoothed Particle Hydrodynamic simulation of hydraulic jump using periodic open boundaries. Appl. Math. Model.
**2016**, 40, 8391–8405. [Google Scholar] [CrossRef] - Chern, M.J.; Syamsuri, S. Effect of corrugated bed on hydraulic jump characteristic using SPH method. J. Hydraul. Eng.
**2012**, 139, 221–232. [Google Scholar] [CrossRef] - Gu, S.; Bo, F.; Luo, M.; Kazemi, E.; Zhang, Y.; Wei, J. SPH Simulation of Hydraulic Jump on Corrugated Riverbeds. Appl. Sci.
**2019**, 9, 436. [Google Scholar] [CrossRef][Green Version] - De Padova, D.; Mossa, M.; Sibilla, S.; Torti, E. 3D SPH modeling of hydraulic jump in a very large channel. J. Hydraul. Res.
**2010**, 51, 158–173. [Google Scholar] [CrossRef] - Chanson, H.; Montes, J.S. Characteristics of undular hydraulic jump: Experimental apparatus and flow patterns. J. Hydraul. Eng.
**1995**, 121, 129–144. [Google Scholar] [CrossRef][Green Version] - Meftah, M.B.; De Serio, F.; Mossa, M.; Pollio, A. Analysis of the velocity field in a large rectangular channel with lateral shockwave. Environ. Fluid Mech.
**2007**, 7, 519–536. [Google Scholar] [CrossRef] - Meftah, M.B.; De Serio, F.; Mossa, M.; Pollio, A. Experimental study of recirculating flows generated by lateral shock waves in very large channels. Environ. Fluid Mech.
**2008**, 8, 215–238. [Google Scholar] [CrossRef] - Meftah, M.B.; Mossa, M.; Pollio, A. Considerations on shock wave/boundary layer interaction in undular hydraulic jumps in horizontal channels with a very high aspect ratio. Eur. J. Mech. B Fluids
**2010**, 29, 415–429. [Google Scholar] [CrossRef] - De Padova, D.; Mossa, M.; Sibilla, S. SPH modelling of hydraulic jump oscillations at an abrupt drop. Water
**2017**, 9, 790. [Google Scholar] [CrossRef][Green Version] - De Padova, D.; Mossa, M.; Sibilla, S. SPH numerical investigation of the characteristics of an oscillating hydraulic jump at an abrupt drop. J. Hydrodyn.
**2018**, 30, 106–113. [Google Scholar] [CrossRef]

**Figure 1.**A hydraulic jump in the large channel of the LIC—Coastal Engineering Laboratory of the Polytechnic University of Bari, Italy. (See Video S1 in Supplementary Material).

**Figure 3.**Hydraulic jump (by Guglielmini [2]).

**Figure 4.**Flow conditions during experiments by Mossa et al. [50]. From the top: (

**a**) A-jump; (

**b**) wave jump; (

**c**) wave train; (

**d**) B-jump (maximum plunging condition); (

**e**) minimum B-jump (limited jump).

**Figure 5.**Oscillatory flow patterns between B-jumps and wave jumps (configuration B61 in Mossa et al. [50]); time is expressed in minutes, seconds, and hundredths of seconds from the start of filming (by Mossa et al. [50]): (

**a**,

**b**,

**g**,

**h**) B-jumps; (

**c**–

**f**) wave jumps. (See Video S2 in Supplementary Material).

**Figure 6.**SPH simulation of hydraulic jump in a very large channel: (

**a**) picture of experiment; (

**b**) wave-height distribution and (

**c**) velocity vector fields.

**Figure 7.**SPH vorticity field; oscillatory flow patterns between A-jumps and wave jumps: (

**a**) t = 2 s; (

**b**) t = 4 s; (

**c**) t = 8.5 s and (

**d**) t = 11.5 s.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Padova, D.; Mossa, M. Hydraulic Jump: A Brief History and Research Challenges. *Water* **2021**, *13*, 1733.
https://doi.org/10.3390/w13131733

**AMA Style**

De Padova D, Mossa M. Hydraulic Jump: A Brief History and Research Challenges. *Water*. 2021; 13(13):1733.
https://doi.org/10.3390/w13131733

**Chicago/Turabian Style**

De Padova, Diana, and Michele Mossa. 2021. "Hydraulic Jump: A Brief History and Research Challenges" *Water* 13, no. 13: 1733.
https://doi.org/10.3390/w13131733