Size and Shape of Steady Seawater Intrusion and Sharp-Interface Wedge: The Polubarinova-Kochina Analytical Solution to the Dam Problem Revisited
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 8
Abstract
Rescaling of the geometrical sizes and the value of hydraulic conductivity in the classical problem of steady two-dimensional (2D) potential seepage through a rectangular earth dam with an empty tailwater is shown to result in a mathematically equivalent problem of seawater intrusion with a sharp interface into a confined horizontal aquifer, which discharges fresh groundwater to the sea through a vertical segment of the beach. The shape of the interface, the vertical and horizontal sizes of the static intrusion wedge, and its cross-sectional area are written in an explicit form, using the Polubarinova-Kochina formulas, rectified. The densities of the two liquids and the aquifers’ hydraulic conductivity and thickness, as well as the incident hydraulic gradient serve as input parameters. With reduction of the incident groundwater gradient far upstream from the intrusion zone (due to, e.g., freshwater abstraction by wells), the sizes of the wedge rapidly increase. The analytical solution has been validated with recent sand tank experiments.
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Acknowledgments
This work was funded by Sultan Qaboos University, the grant SR/SCI/ETHS/11/01; Russian Foundation for Basic Research Grant No. 13-01-00322_a; and through a special program of the Russian Government supporting research at Kazan Federal University. Critique and suggestions by two anonymous reviewers are highly appreciated.
References
Al-Bitar, A., and Ababou, R. (2005). “Random field approach to seawater intrusion in heterogeneous coastal aquifers: Unconditional simulations and statistical analysis.” Geostatistics for environmental applications, P. Renard, H. Demougeot-Renard, and R. Froidevaux, eds., Springer, Heidelberg, Germany, 233–248.
Bakker, M. (2014). “Exact versus Dupuit interface flow in anisotropic coastal aquifers.” Water Resour. Res., 50(10), 7973–7983.
Bear, J., and Dagan, G. (1964). “Some exact solutions of interface problems by means of the hodograph method.” J. Geophys. Res., 69(8), 1563–1572.
Bereslavski, E. N. (2007). “Calculation of the salt-water intrusion in coastal regions of the sea bed.” Doklady Phys., 52(3), 146–150.
Bertorelle, E. (2014). “Laboratory experiments on the saltwater intrusion process.” M.S. thesis, Univ. of Padua, Padua, Italy.
Burnett, W. C., et al. (2006). “Quantifying submarine groundwater discharge in the coastal zone via multiple methods.” Sci. Total Environ., 367(2–3), 498–543.
Chang, S. W., and Clement, T. P. (2012). “Experimental and numerical investigation of saltwater intrusion dynamics in flux-controlled groundwater systems.” Water Resour. Res., 48(9), W09527.
Cheng, A. H.-D., and Ouazar, D. (1999). “Analytical solutions.” Seawater intrusion in coastal aquifers: Concepts, methods and practices, J. Bear, A. H.-D. Cheng, S. Sorek, D. Ouazar, and I. Herrera, eds., Kluwer, Dordrecht, Netherlands.
Crank, J. (1984). Free and moving boundary problems, Oxford University Press, Oxford, U.K.
Craster, R. V. (1994). “Two related free boundary problems.” IMA J. Appl. Math., 52(3), 253–270.
De Josselin De Jong, G., and Van Duijn, C. J. (1984). “Transverse dispersion from an originally sharp fresh-salt interface caused by shear flow.” J. Hydrol., 84(1–2), 55–79.
Detournay, C., and Strack, O. D. L. (1988). “A new approximate technique for the hodograph method in groundwater flow and its application to coastal aquifers.” Water Resour. Res., 24(9), 1971–1981.
Faure, H., Walter, R. C., and Grant, D. R. (2002). “The coastal oasis: Ice age springs on emerged continental shelves.” Global Planet. Change, 33(1–2), 47–56.
Ferguson, G., and Gleeson, T. (2012). “Vulnerability of coastal aquifers to groundwater use and climate change.” Nat. Clim. Changes, 2, 342–345.
Glover, R. E. (1959). “The pattern of freshwater flow in a coastal aquifer.” J. Geophys. Res., 64(4), 457–459.
Goswami, R. R., and Clement, T. P. (2007). “Laboratory-scale investigation of saltwater intrusion dynamics.” Water Resour. Res., 43(4), W04418.
Hocking, G. C., and Forbes, L. K. (2004). “The lens of freshwater in a tropical island—2d withdrawal.” Comput. Fluids, 33(1), 19–30.
Hoefel, F. G., and Evans, R. L. (2001). “Impact of low salinity porewater on seafloor electromagnetic data: A means of detecting submarine groundwater discharge?” Estuarine Coastal Shelf Sci., 52(2), 179–189.
Hornung, U., and Krueger, T. (1985). “Evaluation of the Polubarinova-Kochina formula for the dam problem.” Water Resour. Res., 21(3), 395–398.
Kacimov, A. R., and Obnosov, Y. V. (2001). “Analytical solution for a sharp interface problem in sea water intrusion into a coastal aquifer.” Proc. R. Soc. London A, 457(2016), 3023–3038.
Kacimov, A. R., and Sherif, M. M. (2006). “Sharp interface, one-dimensional seawater intrusion into a confined aquifer with controlled pumping: Analytical solution.” Water Resour. Res., 42(6), W06501.
Kacimov, A. R., Sherif, M. M., Perret, J. S., and Al-Mushikhi, A. (2009). “Control of sea-water intrusion by salt-water pumping: Coast of Oman.” Hydrogeol. J., 17(3), 541–558.
Kashef, A. I. (1983). “Harmonizing Ghyben-Herzberg interface with rigorous solutions.” Ground Water, 21(2), 153–159.
Kourakos, G., and Mantoglou, A. (2015). “An efficient simulation-optimization coupling for management of coastal aquifers.” Hydrogeol. J., 23(6), 1167–1179.
Koussis, A. D., Mazi, K., Riou, F., and Destouni, G. (2015). “A correction for Dupuit-Forchheimer interface flow models of seawater intrusion in unconfined coastal aquifers.” J. Hydrol., 525, 277–285.
Llopis-Albert, C., and Pulido-Velazquez, D. (2015). “Using MODFLOW code to approach transient hydraulic head with a sharp-interface solution.” Hydrol. Processes, 29(8), 2052–2064.
Lu, C., Werner, A. D., Simmons, C. T., and Luo, J. (2015). “A correction on coastal heads for groundwater flow models.” Groundwater, 53(1), 164–170.
Mazi, K., Koussis, A. D., and Destouni, G. (2014). “Intensively exploited Mediterranean aquifers: Resilience and proximity to critical points of seawater intrusion.” Hydrol. Earth Syst. Sci., 18(5), 1663–1677.
Motz, L., and Sedighi, A. (2009). “Representing the coastal boundary condition in regional groundwater flow models.” J. Hydrol. Eng., 821–831.
Paster, A., and Dagan, G. (2008). “Mixing at the interface between fresh and salt waters in 3D steady flow with application to a pumping well in a coastal aquifer.” Adv. Water Resour., 31(12), 1565–1577.
Polubarinova-Kochina, P. Y. (1962). Theory of ground water movement, 1st Ed., Princeton University Press, Princeton, NJ.
Polubarinova-Kochina, P. Y. (1977). Theory of ground water movement, 2nd Ed., Nauka, Moscow.
Sherif, M., Mohamed, M., Kacimov, A., and Shetty, A. (2012). “Modeling groundwater flow and seawater intrusion in the coastal aquifer of Wadi Ham, UAE.” Water Resour. Manage., 26(3), 751–774.
Sherif, M., Sefelnasr, A., Ebraheem, A., and Javadi, A. (2014). “Quantitative and qualitative assessment of seawater intrusion in Wadi Ham under different pumping scenarios.” J. Hydrol. Eng., 855–866.
Strack, O. D. L. (1989). Groundwater mechanics, Prentice Hall, Englewood Cliffs, NJ.
Strack, O. D. L., and Ausk, B. K. (2015). “A formulation for vertically integrated groundwater flow in a stratified coastal aquifer.” Water Resour. Res., 51(8), 6756–6775.
Taniguchi, M., Burnett, W. C., Cable, J. E., and Turner, J. V. (2002). “Investigation of submarine groundwater discharge.” Hydrol. Processes, 16(11), 2115–2129.
Uchiyama, Y., Nadaoka, K., Rolke, P., Adachi, K., and Yagi, H. (2000). “Submarine groundwater discharge into the sea and associated nutrient transport in a sandy beach.” Water Resour. Res., 36(6), 1467–1479.
Werner, A. D., et al. (2012). “Seawater intrusion processes, investigation and management: Recent advances and future challenges.” Adv. Water Resour., 51, 3–26.
Wolfram, S. (1991). Mathematica: A system for doing mathematics by computer, Addison-Wesley, Redwood City, CA.
Zektser, I. S., and Loaiciga, H. A. (1993). “Groundwater fluxes in the global hydrologiccycle: Past, present and future.” J Hydrol., 144(1–4), 405–427.
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Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 8 • August 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 5, 2015
Accepted: Jan 14, 2016
Published online: Mar 29, 2016
Published in print: Aug 1, 2016
Discussion open until: Aug 29, 2016
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