Technical Papers
Jan 22, 2020

Dynamics of Gravity Currents Flowing Up a Slope and Implications for Entrainment

Publication: Journal of Hydraulic Engineering
Volume 146, Issue 4

Abstract

The dynamics of lock-release gravity currents flowing up a sloping bottom are investigated by laboratory experiments. Both full-depth and partial-depth gravity currents are analyzed, and a wide range of bottom slopes are tested. The front evolution is discussed and it is found that the presence of an upslope affects the flow, causing an earlier transition between the different flow regimes. An empirical relation able to predict the length of the slumping phase as a function of the inclination of the sloping bottom and depth ratio of the dense and ambient fluids is proposed. The density fields highlight the presence of a back flow, which, for steep upslopes, is due to the dense current reflected by the upsloping bottom behaving more like an obstacle than as an upsloping bed. In addition, the entrainment of ambient fluid within the dense current is evaluated, and it is observed to decrease as the angle of the upslope increases until it reaches a minimum value, beyond which the density current feels the upslope as an obstacle.

Get full access to this article

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

Acknowledgments

This research was funded by the Italian Ministry of Education, University, and Research (MIUR) through the Departments of Excellence 2018–2022 Program.

References

Adduce, C., G. Sciortino, and S. Proietti. 2012. “Gravity currents produced by lock exchanges: Experiments and simulations with a two-layer shallow-water model with entrainment.” J. Hydraul. Eng. 138 (2): 111–121. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000484.
Alavian, V. 1986. “Behavior of density currents on an incline.” J. Hydraul. Eng. 112 (1): 27–42. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:1(27).
Armenio, V. 2017. “Large eddy simulation in hydraulic engineering: Examples of laboratory-scale numerical experiments.” J. Hydraul. Eng. 143 (11): 03117007. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001357.
Cenedese, C., and C. Adduce. 2008. “Mixing in a density-driven current flowing down a slope in a rotating fluid.” J. Fluid Mech. 604: 369–388. https://doi.org/10.1017/S0022112008001237.
Cenedese, C., and C. Adduce. 2010. “A new parameterization for entrainment in overflows.” J. Phys. Oceanogr. 40: 1835–1850. https://doi.org/10.1175/2010JPO4374.1.
Cuthbertson, A. J., J. Laanearu, A. K. Wåhlin, and P. A. Davies. 2011. “Experimental and analytical investigation of dense gravity currents in a rotating, up-sloping and converging channel.” Dyn. Atmos. Oceans 52 (3): 386–409. https://doi.org/10.1016/j.dynatmoce.2011.09.001.
Dai, A. 2013. “Experiments on gravity currents propagating on different bottom slopes.” J. Fluid Mech. 731: 117–141. https://doi.org/10.1017/jfm.2013.372.
Dai, A. 2015. “High-resolution simulations of downslope gravity currents in the acceleration phase.” Phys. Fluids 27 (7): 076602. https://doi.org/10.1063/1.4923208.
Dai, A., and Y. Huang. 2016. “High-resolution simulations of non-Boussinesq downslope gravity currents in the acceleration phase.” Phys. Fluids 28 (2): 026602. https://doi.org/10.1063/1.4942239.
Dai, A., C. Ozdemir, M. Cantero, and S. Balachandar. 2011. “Gravity currents from instantaneous sources down a slope.” J. Hydraul. Eng. 138 (3): 237–246. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000500.
Ellison, T., and J. Turner. 1959. “Turbulent entrainment in stratified flows.” J. Fluid Mech. 6 (3): 423–448. https://doi.org/10.1017/S0022112059000738.
Garvine, R. W., and J. D. Monk. 1974. “Frontal structure of a river plume.” J. Geophys. Res. 79 (15): 2251–2259. https://doi.org/10.1029/JC079i015p02251.
Geyer, W. 1988. “The advance of a salt wedge front: Observations and dynamical model.” In Physical processes in estuaries, 181–195. New York: Springer.
Hallworth, M. A., H. E. Huppert, J. C. Phillips, and R. S. J. Sparks. 1996. “Entrainment into two-dimensional and axisymmetric turbulent gravity currents.” J. Fluid Mech. 308: 289–311. https://doi.org/10.1017/S0022112096001486.
He, Z., L. Zhao, T. Lin, P. Hu, Y. lv, H.-C. Ho, and Y.-T. Lin. 2017. “Hydrodynamics of gravity currents down a ramp in linearly stratified environments.” J. Hydraul. Eng. 143 (3): 04016085. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001242.
Huppert, H. E., and J. E. Simpson. 1980. “The slumping of gravity currents.” J. Fluid Mech. 99 (4): 785–799. https://doi.org/10.1017/S0022112080000894.
Inghilesi, R., C. Adduce, V. Lombardi, F. Roman, and V. Armenio. 2018. “Axisymmetric three-dimensional gravity currents generated by lock exchange.” J. Fluid Mech. 851: 507–544. https://doi.org/10.1017/jfm.2018.500.
Laanearu, J., A. J. Cuthbertson, and P. A. Davies. 2014. “Dynamics of dense gravity currents and mixing in an up-sloping and converging vee-shaped channel.” J. Hydraul. Res. 52 (1): 67–80. https://doi.org/10.1080/00221686.2013.841779.
La Forgia, G., C. Adduce, and F. Falcini. 2018a. “Laboratory investigation on internal solitary waves interacting with a uniform slope.” Adv. Water Res. 120 (Oct): 4–18. https://doi.org/10.1016/j.advwatres.2017.07.027.
La Forgia, G., C. Adduce, F. Falcini, and C. Paola. 2019. “Migrating bedforms generated by solitary waves.” Geophys. Res. Lett. 46 (9): 4738–4746. https://doi.org/10.1029/2019GL082511.
La Forgia, G., T. Tokyay, C. Adduce, and G. Constantinescu. 2018b. “Numerical investigation of breaking internal solitary waves.” Phys. Rev. Fluids 3 (10): 104801. https://doi.org/10.1103/PhysRevFluids.3.104801.
La Rocca, M., P. Prestininzi, C. Adduce, G. Sciortino, and R. Hinkelmann. 2013. “Lattice Boltzmann simulation of 3D gravity currents around obstacles.” Int. J. Offshore Polar Eng. 23 (3): 178–185.
Lombardi, V., C. Adduce, and M. La Rocca. 2018. “Unconfined lock-exchange gravity currents with variable lock width: Laboratory experiments and shallow-water simulations.” J. Hydraul. Res. 56 (3): 399–411. https://doi.org/10.1080/00221686.2017.1372817.
Lombardi, V., C. Adduce, G. Sciortino, and M. La Rocca. 2015. “Gravity currents flowing upslope: Laboratory experiments and shallow water simulations.” Phys. Fluids 27 (1): 016602. https://doi.org/10.1063/1.4905305.
Lu, R., and R. P. Turco. 1994. “Air pollutant transport in a coastal environment. Part I: Two-dimensional simulations of sea-breeze and mountain effects.” J. Atmos. Sci. 51 (15): 2285–2308. https://doi.org/10.1175/1520-0469(1994)051%3C2285:APTIAC%3E2.0.CO;2.
Marino, B., L. Thomas, and P. Linden. 2005. “The front condition for gravity currents.” J. Fluid Mech. 536: 49–78. https://doi.org/10.1017/S0022112005004933.
Marleau, L. J., M. R. Flynn, and B. R. Sutherland. 2014. “Gravity currents propagating up a slope.” Phys. Fluids 26 (4): 046605. https://doi.org/10.1063/1.4872222.
Musumeci, R. E., A. Viviano, and E. Foti. 2017. “Influence of regular surface waves on the propagation of gravity currents: Experimental and numerical modeling.” J. Hydraul. Eng. 143 (8): 04017022. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001308.
Nogueira, H. I., C. Adduce, E. Alves, and M. J. Franca. 2013a. “Analysis of lock-exchange gravity currents over smooth and rough beds.” J. Hydraul. Res. 51 (4): 417–431. https://doi.org/10.1080/00221686.2013.798363.
Nogueira, H. I., C. Adduce, E. Alves, and M. J. Franca. 2013b. “Image analysis technique applied to lock-exchange gravity currents.” Meas. Sci. Technol. 24 (4): 047001. https://doi.org/10.1088/0957-0233/24/4/047001.
Nogueira, H. I., C. Adduce, E. Alves, and M. J. Franca. 2014. “Dynamics of the head of gravity currents.” Environ. Fluid Mech. 14: 519–540. https://doi.org/10.1007/s10652-013-9315-2.
Nogueira, H. I., P. van der Ven, T. O’Mahoney, A. De Loor, A. van der Hout, and W. Kortlever. 2018. “Effect of density differences on the forces acting on a moored vessel while operating navigation locks.” J. Hydraul. Eng. 144 (6): 04018021. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001445.
Ooi, S. K., G. Constantinescu, and L. J. Weber. 2007. “2D large-eddy simulation of lock-exchange gravity current flows at high Grashof numbers.” J. Hydraul. Eng. 133 (9): 1037–1047. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:9(1037).
Ooi, S. K., G. Constantinescu, and L. J. Weber. 2009. “Numerical simulations of lock-exchange compositional gravity current.” J. Fluid Mech. 635: 361–388. https://doi.org/10.1017/S0022112009007599.
Ottolenghi, L., C. Adduce, R. Inghilesi, F. Roman, and V. Armenio. 2016. “Mixing in lock-release gravity currents propagating up a slope.” Phys. Fluids 28 (5): 056604. https://doi.org/10.1063/1.4948760.
Ottolenghi, L., C. Adduce, F. Roman, and V. Armenio. 2017a. “Analysis of the flow in gravity currents propagating up a slope.” Ocean Modell. 115 (Jul): 1–13. https://doi.org/10.1016/j.ocemod.2017.05.001.
Ottolenghi, L., C. Cenedese, and C. Adduce. 2017b. “Entrainment in a dense current flowing down a rough sloping bottom in a rotating fluid.” J. Phys. Oceanogr. 47 (3): 485–498. https://doi.org/10.1175/JPO-D-16-0175.1.
Ottolenghi, L., P. Prestininzi, A. Montessori, C. Adduce, and M. La Rocca. 2018. “Lattice Boltzmann simulations of gravity currents.” Eur. J. Mech.-B/Fluids 67 (Jan–Feb): 125–136. https://doi.org/10.1016/j.euromechflu.2017.09.003.
Pérez-Díaz, B., S. Castanedo, P. Palomar, F. Henno, and M. Wood. 2019. “Modeling nonconfined density currents using 3D hydrodynamic models.” J. Hydraul. Eng. 145 (3): 04018088. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001563.
Pérez-Díaz, B., P. Palomar, S. Castanedo, and A. Álvarez. 2018. “PIV-PLIF characterization of nonconfined saline density currents under different flow conditions.” J. Hydraul. Eng. 144 (9): 04018063. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001511.
Rottman, J. W., and J. E. Simpson. 1983. “Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel.” J. Fluid Mech. 135: 95–110. https://doi.org/10.1017/S0022112083002979.
Schijf, J., and J. Schönfled. 1953. “Theoretical considerations on the motion of salt and fresh water.” In Proc., Minnesota Int. Hydraulic Convention, 321–333. Madrid, Spain: International Association for Hydro-Environment Engineering and Research.
Simpson, J. E. 1994. Sea breeze and local winds. Cambridge, UK: Cambridge University Press.
Simpson, J. E. 1997. Gravity currents: In the environment and the laboratory. Cambridge, UK: Cambridge University Press.
Stancanelli, L., R. Musumeci, and E. Foti. 2018. “Dynamics of gravity currents in the presence of surface waves.” J. Geophys. Res.: Oceans 123 (3): 2254–2273. https://doi.org/10.1002/2017JC013273.
Steenhauer, K., T. Tokyay, and G. Constantinescu. 2017. “Dynamics and structure of planar gravity currents propagating down an inclined surface.” Phys. Fluids 29 (3): 036604. https://doi.org/10.1063/1.4979063.
Sutherland, B., K. Barrett, and G. Ivey. 2013. “Shoaling internal solitary waves.” J. Geophys. Res.: Oceans 118 (9): 4111–4124. https://doi.org/10.1002/jgrc.20291.
Theiler, Q., and M. J. Franca. 2016. “Contained density currents with high volume of release.” Sedimentology 63 (6): 1820–1842. https://doi.org/10.1111/sed.12295.
Tokyay, T., G. Constantinescu, and E. Meiburg. 2011. “Lock-exchange gravity currents with a high volume of release propagating over a periodic array of obstacles.” J. Fluid Mech. 672: 570–605. https://doi.org/10.1017/S0022112010006312.
Tokyay, T., G. Constantinescu, and E. Meiburg. 2014. “Lock-exchange gravity currents with a low volume of release propagating over an array of obstacles.” J. Geophys. Res.: Oceans 119 (5): 2752–2768. https://doi.org/10.1002/2013JC009721.
Turner, J. 1986. “Turbulent entrainment: The development of the entrainment assumption and its application to geophysical flows.” J. Fluid Mech. 173: 431–471. https://doi.org/10.1017/S0022112086001222.
Wilson, R. I., H. Friedrich, and C. Stevens. 2019. “Quantifying propagation characteristics of unconfined turbidity currents interacting with an obstacle within the slumping regime.” J. Hydraul. Res. 57 (4): 498–516. https://doi.org/10.1080/00221686.2018.1494054.
Zhao, L., Z. He, Y. Lv, Y.-T. Lin, P. Hu, and T. Pähtz. 2018. “Front velocity and front location of lock-exchange gravity currents descending a slope in a linearly stratified environment.” J. Hydraul. Eng. 144 (11): 04018068. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001536.
Zordan, J., A. Schleiss, and M. Franca. 2018. “Structure of a dense release produced by varying initial conditions.” Environ. Fluid Mech. 18 (5): 1101–1119. https://doi.org/10.1007/s10652-018-9586-8.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 146Issue 4April 2020

History

Received: Jan 27, 2019
Accepted: Aug 23, 2019
Published online: Jan 22, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 22, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

M. C. De Falco [email protected]
Ph.D. Student, Dept. of Engineering, Univ. Roma Tre, Via Vito Volterra 62, 00146 Rome, Italy. Email: [email protected]
L. Ottolenghi, Ph.D. [email protected]
High Council for Public Works, Ministry of Infrastructure and Transport, Via Nomentana 2, 00161 Rome, Italy. Email: [email protected]
Associate Professor, Dept. of Engineering, Univ. Roma Tre, Via Vito Volterra 62, 00146 Rome, Italy (corresponding author). ORCID: https://orcid.org/0000-0002-0734-9569. 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