Abstract

This paper presents a new method that is able to define the hydraulic jump peculiarities in rough-bed conditions. The findings of this paper improve the literature and guidelines on the design of a stilling basin over a rough bed, taking into account both the Froude number and bottom roughness. It starts with experimental evidence on the flow field and considers the characteristic length scale of the phenomenon as drawn from velocity measurements in the hydraulic jump region. The assumption in the length scale leads to different results compared with the known formulas in the literature related to the hydraulic jump on a rough bed. The formulas in the literature consider the effects of gravel roughness only, neglecting the effects due to the incident Froude number in the evaluation of integrated bottom shear stress. The comparison of the presented results with experimental measurements in the literature highlights the reliability and accuracy of this novel method. This method is theoretically based, but because it needs experimental data in application, it can be considered semiempirical. The results presented here allow for the design of hydraulic jump stilling basins over rough beds.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

References

Barjastehmaleki, S. 2016. “Spillway stilling basins and plunge pools lining design.” Ph.D. thesis, Dept. of Engineering and Architecture, Univ. of Trieste.
Barjastehmaleki, S., V. Fiorotto, and E. Caroni. 2015. “Stochastic analysis of pressure field in hydraulic jump region via Taylor hypothesis.” In Proc., 36th IAHR World Congress, 1–12. Madrid, Spain: International Association for Hydro-Environment Engineering and Research.
Barjastehmaleki, S., V. Fiorotto, and E. Caroni. 2016a. “Design of stilling basin linings with sealed and unsealed joints.” J. Hydraul. Eng. 142 (12): 04016064. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001218.
Barjastehmaleki, S., V. Fiorotto, and E. Caroni. 2016b. “Spillway stilling basins lining design via Taylor hypothesis.” J. Hydraul. Eng. 142 (6): 04016010. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001133.
Bathurst, J. C., and D. B. Simons. 1981. “Resistance equation for large scale roughness.” J. Hydraul. Div. 107 (12): 1593–1613.
Carollo, F. G., and V. Ferro. 2004. “Determinazione delle altezze coniugate del risalto libero su fondo liscio e scabro.” [In Italian.] Rivista di Ingegnaria Agraria 35 (4): 1–11.
Carollo, F. G., V. Ferro, and V. Pampalone. 2007. “Hydraulic jumps on rough beds.” J. Hydraul. Eng. 133 (9): 989–999. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:9(989).
Cheng, N. S. 2017. “Simple modification of Manning-Strickler formula for large-scale roughness.” J. Hydraul. Eng. 143 (9): 1–8. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001345.
Chow, V. T. 1959. Open channel hydraulics. New York: McGraw-Hill.
Dey, S., and A. Sarkar. 2006. “Response of velocity and turbulence in submerged wall jets to abrupt changes from smooth to rough beds and its application to scour downstream of an apron.” J. Fluid Mech. 556: 387–419. https://doi.org/10.1017/S0022112006009530.
Dey, S., and A. Sarkar. 2007. “Computation of Reynolds and boundary shear stress in submerged jets on rough boundaries.” J. Hydro-Environ. Res. 1 (Dec): 110–117. https://doi.org/10.1016/j.jher.2007.10.001.
Ead, S. A., and N. Rajaratman. 2002. “Hydraulic jumps on corrugated beds.” J. Hydraul. Eng. 128 (7): 656–663. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:7(656).
Fiorotto, V., and A. Rinaldo. 1992a. “Fluctuating uplift and lining design in spillway stilling basins.” J. Hydraul. Res. 118 (4): 578–596. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:4(578).
Fiorotto, V., and A. Rinaldo. 1992b. “Turbulent pressure fluctuations under hydraulic jump.” J. Hydraul. Res. 30 (4): 499–520. https://doi.org/10.1080/00221689209498897.
Hager, W. H. 1992. Energy dissipator and hydraulic jump, 288. Dordrecht, Netherlands: Kluwer Academic.
Hager, W. H., R. Bremen, and N. Kawagoshi. 1990. “Classical hydraulic jump: Length of roller.” J. Hydraul. Res. 28 (5): 591–608. https://doi.org/10.1080/00221689009499048.
Hughes, W. C., and J. E. Flack. 1984. “Hydraulic jump properties over a rough bed.” J. Hydraul. Eng. 110 (12): 1755–1771. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:12(1755).
Liu, M., N. Rajaratnam, and D. Zhu. 2004. “Turbulence structure of hydraulic jumps of low Froude numbers.” J. Hydraul. Eng. 130 (6): 511–520. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:6(511).
Long, D., P. Steffler, and N. Rajaratnam. 1990. “LDA study of flow structure in submerged hydraulic jump.” J. Hydraul. Res. 28 (4): 437–460. https://doi.org/10.1080/00221689009499059.
Ohtsu, L., Y. Yasuda, and S. Awazu. 1990. Free and submerged hydraulic jumps in rectangular channels. Tokyo: Nihon Univ.
Pagliara, S., and D. Dazzini. 2002. “Hydraulics of block ramp for river restoration.” In Proc., 2nd Int. Conf., 1–15. Milan, Italy: Centro Studi Idraulica Urbana.
Pagliara, S., I. Lotti, and M. Palermo. 2008. “Hydraulic jumps on rough bed of stream rehabilitation structures.” J. Hydro-Enviro Res. 2 (1): 29–38. https://doi.org/10.1016/j.jher.2008.06.001.
Pagliara, S., and M. Palermo. 2015. “Hydraulic jump on rough and smooth beds: Aggregate approach for horizontal and adverse-sloped beds.” J. Hydraul. Res. 53 (2): 243–252. https://doi.org/10.1080/00221686.2015.1017778.
Palermo, M., and S. Pagliara. 2017. “D-jump in rough sloping channel at low Froude number.” J. Hydro-Enviro Res. 14 (1): 150–156. https://doi.org/10.1016/j.jher.2016.10.002.
Palermo, M., and S. Pagliara. 2018. “Semi-theoretical approach for energy dissipation at hydraulic jumps in rough sloped channels.” J. Hydraul. Res. 56 (6): 786–795. https://doi.org/10.1080/00221686.2017.1419991.
Rajaratnam, N. 1965. “The hydraulic jump as a wall jet.” J. Hydraul. Div. 91 (5): 107–132.
Rajaratnam, N. 1968. “Hydraulic jumps on rough beds.” Trans. Eng. Inst. Canada 11 (A-2): 1–8.
Schroder, R. 1963. Die turbulente Strömung im freien Wechselsprung: Habilitationsschrift, Mitteilung 59. Berlin: Institut für Wasserbau und Wasserwirtschaft.
Schwarz, W. H., and W. P. Cosart. 1961. “The two dimensional turbulent wall jet.” J. Fluid Mech. 10 (4): 481–495. https://doi.org/10.1017/S0022112061000299.
Smart, G. M., M. J. Duncan, and J. M. Walsh. 2002. “Relatively rough flow resistance equation.” J. Hydraul. Eng. 128 (6): 568–578. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:6(568).
USBR (US Bureau of Reclamation). 1984. Hydraulic design of stilling basins and energy dissipater. Engineering Monograph No. 25. Denver: USBR.
Vyzgo, M. S., and Y. M. Kuz’minov. 1963. Change in length of hydraulic jump with changes of channel bottom roughness. Translated by F. Phillip. Washington, DC: US Dept. of the Interior Bureau of Reclamation.
Witheridge, G. 2011. “Background to rock roughness equation.” Waterway Manage. Pract.
Wu, S., and N. Rajaratnam. 1995. “Free jumps, submerged jumps and wall jets.” J. Hydraul. Res. 33 (2): 197–212. https://doi.org/10.1080/00221689509498670.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 147Issue 1January 2021

History

Received: Sep 30, 2019
Accepted: Jul 13, 2020
Published online: Oct 19, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 19, 2021

Permissions

Request permissions for this article.

Authors

Affiliations

Lead Dams and Principal Engineer, Sunwater, Green Square North, Level 9, 515 St Pauls Terrace, Fortitude Valley, QLD 4006, Australia (corresponding author). ORCID: https://orcid.org/0000-0001-9704-4744. Email: [email protected]
Formerly, Professor, Dept. of Engineering and Architecture, Univ. of Trieste, Piazzale Europa, 1, Trieste 34100, Italy. ORCID: https://orcid.org/0000-0002-4733-9824. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share