Front Velocity and Front Location of Lock-Exchange Gravity Currents Descending a Slope in a Linearly Stratified Environment
Publication: Journal of Hydraulic Engineering
Volume 144, Issue 11
Abstract
Gravity currents descending a slope in a linearly stratified environment can be frequently encountered in nature. However, few studies have quantitatively investigated the evolution process of lock-exchange gravity currents in such environments. A new set of analytical formulae is proposed by integrating both mass conservation and linear momentum equations to determine the front velocity and the front location of a downslope current. Based on the thermal theory, the formula considers the influence of ambient stratification by introducing a newly defined stratification coefficient in the acceleration stage. As for the deceleration stage, the formula is derived by adding a parameter that takes into account the density distribution of the ambient water. The transition point between the acceleration and deceleration stages and the maximum front velocity are also determined by the proposed formulae. Lock-exchange gravity current experiments are conducted in the flume with linear stratifications to provide data for the validation of the formulae. The comparisons between the calculated and measured data in terms of front location and front velocity show satisfactory agreements, which reveal that front velocity presents a rapid acceleration stage and then a deceleration stage in a linearly stratified ambient.
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Acknowledgments
This work was partially supported by the National Key Research and Development Program of China (2017YFC0405502), National Natural Science Foundation of China (11672267), Natural Science Foundation of Zhejiang Province (LR16E090001), and Research Funding of Shenzhen City (JCYJ20160425164642646).
References
Baines, P. G. 2001. “Mixing in flows down gentle slopes into stratified environments.” J. Fluid Mech. 443: 237–270. https://doi.org/10.1017/S0022112001005250.
Batchelor, G. K. 2000. An introduction to fluid dynamics. Cambridge, UK: Cambridge University Press.
Beghin, P., E. J. Hopfinger, and R. E. Britter. 1981. “Gravitational convection from instantaneous sources on inclined boundaries.” J. Fluid Mech. 107: 407–422. https://doi.org/10.1017/S0022112081001821.
Benjamin, T. B. 1968. “Gravity currents and related phenomena.” J. Fluid Mech. 31 (2): 209–248. https://doi.org/10.1017/S0022112068000133.
Birman, V. K., E. Meiburg, and M. Ungarish. 2007. “On gravity currents in stratified ambients.” Phys. Fluids 19 (8): 86602. https://doi.org/10.1063/1.2756553.
Cortés, A., F. J. Rueda, and M. G. Wells. 2014. “Experimental observations of the splitting of a gravity current at a density step in a stratified water body.” J. Geophys. Res. Oceans 119 (2): 1038–1053. https://doi.org/10.1002/2013JC009304.
Dade, W. B., J. R. Lister, and H. E. Huppert. 1994. “Fine-sediment deposition from gravity surges on uniform slopes.” J. Sediment Res. 64 (3): 423–432. https://doi.org/10.1306/D4267DD4-2B26-11D7-8648000102C1865D.
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. 2014. “Non-Boussinesq gravity currents propagating on different bottom slopes.” J. Fluid Mech. 741: 658–680. https://doi.org/10.1017/jfm.2014.5.
Dai, A. 2015. “Thermal theory for non-Boussinesq gravity currents propagating on inclined boundaries.” J. Hydraul. Eng. 141 (1): 6014021. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000949.
Ellison, T. H., and J. S. Turner. 1959. “Turbulent entrainment in stratified flows.” J. Fluid Mech. 6 (3): 423–448. https://doi.org/10.1017/S0022112059000738.
Fernandez, R. L., and J. Imberger. 2008. “Time-varying underflow into a continuous stratification with bottom slope.” J. Hydraul Eng. 134 (9): 1191–1198. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:9(1191).
Ghajar, A. J., and K. Bang. 1993. “Experimental and analytical studies of different methods for producing stratified flows.” Energy 18 (4): 323–334. https://doi.org/10.1016/0360-5442(93)90067-N.
Guo, Y., Z. Zhang, and B. Shi. 2014. “Numerical simulation of gravity current descending a slope into a linearly stratified environment.” J. Hydraul. Eng. 140 (12): 4014061. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000936.
He, Z., L. Zhao, T. Lin, P. Hu, Y. Lv, H. Ho, and Y. Lin. 2017. “Hydrodynamics of gravity currents down a ramp in linearly stratified environments.” J. Hydraul. Eng. 143 (3): 4016085. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001242.
Ho, H., and Y. Lin. 2015. “Gravity currents over a rigid and emergent vegetated slope.” Adv. Water Resour. 76: 72–80. https://doi.org/10.1016/j.advwatres.2014.12.005.
Huppert, H. E., and J. E. Simpson. 1980. “The slumping of gravity currents.” J. Fluid Mech. 99 (04): 785–799. https://doi.org/10.1017/S0022112080000894.
Ieong, K. K., K. M. Mok, and H. Yeh. 2006. “Fluctuation of the front propagation speed of developed gravity current.” Supplement, J. Hydrodyn. Ser. B 18 (S3): 351–355. https://doi.org/10.1016/S1001-6058(06)60077-2.
Longo, S., M. Ungarish, V. Di Federico, L. Chiapponi, and F. Addona. 2016. “Gravity currents in a linearly stratified ambient fluid created by lock release and influx in semi-circular and rectangular channels.” Phys. Fluids 28 (9): 96602. https://doi.org/10.1063/1.4963009.
Maxworthy, T. 2010. “Experiments on gravity currents propagating down slopes. Part 2: The evolution of a fixed volume of fluid released from closed locks into a long, open channel.” J. Fluid Mech. 647: 27–51. https://doi.org/10.1017/S0022112009006065.
Maxworthy, T., J. Leilich, J. E. Simpson, and E. H. Meiburg. 2002. “The propagation of a gravity current into a linearly stratified fluid.” J. Fluid Mech. 453: 371–394. https://doi.org/10.1017/S0022112001007054.
Maxworthy, T., and R. I. Nokes. 2007. “Experiments on gravity currents propagating down slopes. Part 1: The release of a fixed volume of heavy fluid from an enclosed lock into an open channel.” J. Fluid Mech. 584: 433–453. https://doi.org/10.1017/S0022112007006702.
Meiburg, E., S. Radhakrishnan, and M. Nasr-Azadani. 2015. “Modeling gravity and turbidity currents: Computational approaches and challenges.” Appl. Mech. Rev. 67 (4): 40802. https://doi.org/10.1115/1.4031040.
Ottolenghi, L., C. Adduce, R. Inghilesi, V. Armenio, and F. Roman. 2016. “Entrainment and mixing in unsteady gravity currents.” J. Hydraul. Res. 54 (5): 541–557. https://doi.org/10.1080/00221686.2016.1174961.
Rastello, M., and E. J. Hopfinger. 2004. “Sediment-entraining suspension clouds: A model of powder-snow avalanches.” J. Fluid Mech. 509: 181–206. https://doi.org/10.1017/S0022112004009322.
Samothrakis, P., and A. J. Cotel. 2006. “Finite volume gravity currents impinging on a stratified interface.” Exp. Fluids 41 (6): 991–1003. https://doi.org/10.1007/s00348-006-0222-x.
Simpson, J. E. 1982. “Gravity currents in the laboratory, atmosphere, and ocean.” Annu. Rev. Fluid Mech. 14 (1): 213–234. https://doi.org/10.1146/annurev.fl.14.010182.001241.
Snow, K., and B. R. Sutherland. 2014. “Particle-laden flow down a slope in uniform stratification.” J. Fluid Mech. 755: 251–273. https://doi.org/10.1017/jfm.2014.413.
Steenhauer, K., T. Tokyay, and G. Constantinescu. 2017. “Dynamics and structure of planar gravity currents propagating down an inclined surface.” Phys. Fluids 29 (3): 36604. https://doi.org/10.1063/1.4979063.
Ungarish, M. 2006. “On gravity currents in a linearly stratified ambient: A generalization of Benjamin’s steady-state propagation results.” J. Fluid Mech. 548: 49–68. https://doi.org/10.1017/S0022112005007421.
Wells, M., and P. Nadarajah. 2009. “The intrusion depth of density currents flowing into stratified water bodies.” J. Phys. Oceanogr. 39 (8): 1935–1947. https://doi.org/10.1175/2009JPO4022.1.
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Published In
Journal of Hydraulic Engineering
Volume 144 • Issue 11 • November 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Sep 21, 2017
Accepted: Jun 5, 2018
Published online: Sep 13, 2018
Published in print: Nov 1, 2018
Discussion open until: Feb 13, 2019
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