TECHNICAL NOTES
Nov 9, 2009

Energy Dissipative Plunging Flows

Publication: Journal of Hydraulic Engineering
Volume 136, Issue 8

Abstract

The analysis of plunging flows using energy dissipation hypothesis is presented in this paper. The classic two-control-volume theory has recently been found questionable and needs to be corrected. In this study, we avoid the questionable part of that framework and use a single control volume for the analysis of plunging flows. Furthermore, we hypothesize that the increase in kinetic energy in the underflow and entrained flow should be no greater than the loss in potential energy as the inflow plunges. In the current framework, the entrained flow rate does not exceed approximately 40% of the total inflow rate. The densimetric Froude number at the plunge point, Fdp=q/gHp3 , where q=inflow rate per unit width; g=reduced gravity of inflow; and Hp=flow depth at the plunge point, is typically in the range of 0.3<Fdp<0.6 for plunging flows in a constant width channel.

Get full access to this article

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

References

Akiyama, J., and Stefan, H. (1984). “Plunging flow into a reservoir: Theory.” J. Hydraul. Eng., 110(4), 484–499.
Benjamin, T. B. (1968). “Gravity currents and related phenomena.” J. Fluid Mech., 31, 209–248.
Bournet, P., Dartus, D., Tassin, B., and Vincon-Leite, B. (1999). “Numerical investigation of plunging density current.” J. Hydraul. Eng., 125(6), 584–594.
Dai, A., Cantero, M. I., and Garcia, M. H. (2007). “Plunging of two-dimensional gravity currents.” 5th Int. Symp. on Environmental Hydraulics, IAHR, Tempe, Ariz.
Dai, A., and Garcia, M. H. (2009). “Discussion of ‘Note on the analysis of plunging of density flows’ by G. Parker and H. Toniolo.” J. Hydraul. Eng., 135(6), 532–533.
Dallimore, C. J., Imberger, J., and Hodges, B. R. (2004). “Modeling a plunging underflow.” J. Hydraul. Eng., 130(11), 1068–1076.
Farrell, G. J., and Stefan, H. (1988). “Mathematical modeling of plunging reservoir flows.” J. Hydraul. Res., 26(5), 525–537.
Ford, D. E., Johnson, M. C., and Monismith, S. G. (1980). “Density inflows to Degray Lake, Arkansas.” 2nd Int. Symp. on Stratified Flows, IAHR, Trondheim, Norway.
Gu, L., and Lawrence, G. A. (2005). “Analytical solution for maximal frictional two-layer exchange flow.” J. Fluid Mech., 543, 1–17.
Hauenstein, W., and Dracos, T. H. (1984). “Investigation of plunging density currents generated by inflows in lakes.” J. Hydraul. Res., 22, 157–179.
Hebbert, B., Imberger, J., Loh, I., and Patterson, J. (1979). “Collie River underflow into the Wellington Reservoir.” J. Hydr. Div., 105(5), 533–545.
Jain, S. C. (1981). “Plunging phenomena in reservoirs.” Proc., Symp. on Surface Water Impoundments, ASCE, Minneapolis, 1249–1257.
Johnson, T. R., Ellis, C. R., and Stefan, H. G. (1989). “Negatively buoyant flow in a diverging channel. Part IV: Entrainment and dilution.” J. Hydraul. Eng., 115, 437–456.
Parker, G., Garcia, M. H., Fukushima, Y., and Yu, W. (1987). “Experiments on turbidity currents over an erodible bed.” J. Hydraul. Res., 25, 123–147.
Parker, G., and Toniolo, H. (2007). “Note on the analysis of plunging of density flows.” J. Hydraul. Eng., 133(6), 690–694.
Savage, S. B., and Brimberg, J. (1975). “Analysis of plunging phenomena in water reservoirs.” J. Hydraul. Res., 13(2), 187–205.
Shin, J. O., Dalziel, S. B., and Linden, P. F. (2004). “Gravity currents produced by lock exchange.” J. Fluid Mech., 521, 1–34.
Simpson, J. (1997). Gravity currents, 2nd Ed., Cambridge University Press, Cambridge, U.K.
Singh, B., and Shah, C. R. (1971). “Plunging phenomenon of density currents in reservoirs.” Houille Blanche, 26(1), 59–64.
Wilkinson, D. L. (1972). “Dynamics of contained oil slicks.” J. Hydr. Div., 98, 1013–1030.
Zaremba, L. J., Lawrence, G. A., and Pieters, R. (2003). “Frictional two-layer exchange flow.” J. Fluid Mech., 474, 339–354.
Zhu, D. Z., and Lawrence, G. A. (1998). “Non-hydrostatic effects in layered shallow water flows.” J. Fluid Mech., 355, 1–16.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 136Issue 8August 2010
Pages: 519 - 523

History

Received: Apr 15, 2008
Accepted: Oct 14, 2009
Published online: Nov 9, 2009
Published in print: Aug 2010

Permissions

Request permissions for this article.

Authors

Affiliations

Albert Dai
Assistant Professor, Dept. of Water Resources and Environmental Engineering, Tamkang Univ., Taipei County 25137, Taiwan (corresponding author).
Marcelo H. García, M.ASCE
Siess Professor and Director, Ven Te Chow Hydrosystems Laboratory, Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana-Champaign, 205 N. Mathews, Urbana, IL 61801.

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