Abstract
A new explicit analytical solution is obtained to a steady-state abrupt interface problem concerning sea-water intrusion into a coastal unconfined homogeneous aquifer with a horizontal impermeable bed and uniformly distributed losses along a phreatic surface. Two free surfaces (encroachment tongue and groundwater table) intersect with a horizontal water table of the resting sea water propagated inland. In the hodograph plane the image of the physical domain is a curvilinear triangle. Conformal mappings of the physical domain and of an unknown complex-potential domain onto an auxiliary half-plane are obtained by a modified method of Polubarinova-Kochina, which is mathematically reduced to a vector Riemann boundary-value problem. Free surfaces are reconstructed for different values of losses, densities of the two fluids, sea water and incident groundwater hydraulic heads. Comparisons with the Dupuit–Forcheimer (hydraulic) model are made and practical implications for catchment-scale groundwater management in Oman and UAE are discussed.
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References
Sea Water Intrusion Beneath the Batinah Coast, 1983–1995. Sultanate of Oman Ministry of Water Resources. Muscat: International Printing Press (1996).
Wadi Bih Dam and Groundwater Recharge Facilities, Volume I Design. Electrowatt Engineering Services Ltd. Ministry of Agriculture and Fisheries, UAE (1981).
Segol G. (1994). Classic Groundwater Simulations: Proving and Improving Numerical Models. Prentice Hall, Englewood Cliffs, 531 pp.
Bear J. (1979). Hydraulics of Groundwater. McGraw-Hill, NewYork, 567 pp.
Kacimov A.R. and Obnosov Yu.V. (2001). Analytical solution for a sharp interface problem in sea water intrusion into a coastal aquifer. Proc R Soc London A 457:3023–3038
Strack O.D.L. (1989). Groundwater Mechanics. Prentice Hall, Englewood Cliffs, 732 pp.
Verruijt A. (1982). Theory of Groundwater Flow. Macmillan, London, 144 pp.
Eastern Batinah Resource Assessment. Progress Report N1. Sultanate of Oman Ministry of Water Resources (1995).
Yechieli Y., Wood W.W. (2002). Hydrogeologic processes in saline systems: playas, sabkhas, and saline lakes. Earth-Science Rev 58: 343–365
Al-Mushikhi A.A.M. Formation of Subsurface Water of the East-south Batinah Region (Sultanate of Oman) and Perspectives of Development. PhD thesis, Moscow State Geoexploration University, Moscow (2002) (in Russian) 146 pp.
Kacimov A.R., Youngs E.G. (2005). Steady-state water-table depressions caused by evaporation in lands overlying a water-bearing substratum. J. Hydrol. Eng. ASCE 10:295–301
Polubarinova-Kochina P.Ya. (1977). Theory of Ground-Water Movement. Nauka, Moscow (in Russian) 664 pp.
Kacimov A.R., Obnosov Yu.V. (2001). Analytical solutions to hydrodynamic problems for oil and gas traps. J. Hydrol 254:33–46
Youngs E.G. (2002). Maintaining fresh-water aquifers over saline water in coastal aquifers. Sultan Qaboos Univ. J. Agricult. Sci. 7:23–28
Howison S.D., King J.R. (1989). Explicit solutions to six free-boundary problems in fluid flow and diffusion. IMA J. Appl. Math. 42:155–175
Bakker M. (1997). Groundwater flow with free boundaries using the hodograph method. Adv. Water Res. 20:207–216
Cummings L.J. (1999). Flow around a wedge of arbitrary angle in a Hele-Shaw cell. Eur. J. Appl. Math. 10:547–560
Kacimov A.R., Yakimov N.D. (2001). Moving phreatic surface in a porous slab: an analytical solution. J. Engng. Math. 40:399–411
Kacimov A.R. and Obnosov Yu.V. (2002). Analytical determination of seeping soil slopes of a constant exit gradient. Zeitschr. Angew. Math. Mech. (Z.A.M.M.) 82:363–376
Kacimov A.R., Obnosov Yu.V., Perret J. (2004). Phreatic surface from a near-reservoir saturated tongue. J. Hydrol. 296: 271–281
Obnosov Yu.V. (1994). Explicit solution of certain problem of R-linear conjugation for a regular triangular chess field. Russian Math. 38:43–64
A.R. Tsitskishvili, Methods of solution of a class of plane problems of the theory of filtration. In: V.N. Emikh (ed.), Mathematical Models of Filtration and Their Applications. Novosibirsk: Institute of Hydrodynamics (1999) (in Russian) pp. 177–188.
Abramowitz M., Stegun I.A. (1970). Handbook of Mathematical Functions. Dover, New York, 1046 pp.
Gradshteyn I.S., Ryzhik I. (1980). Tables of Integrals, Series and Products. Academic Press, New York, 1060 pp.
Wolfram S. (1991). Mathematica A System for Doing Mathematics by Computer. Addison-Wesley, Redwood City, 961 pp.
Strack O.D.L., Asgian M.I. (1978). A new function for the use in the hodograph method. Water Resour. Res. 14:1045–1058
Youngs E.G. (1990). An examination of computed steady-state water-table heights in unconfined aquifers: Dupuit-Forchheimer estimates and exact analytical results. J. Hydrol. 119:201–214
Kacimov A.R. (2003). Unsaturated quasi-linear flow analysis in V-shaped domains. J. Hydrol. 279:70–82
A.R. Kacimov, M.M. Sherif, J.S. Perret and A. Al-Mushikhi. Sea water intrusion in an unconfined coastal aquifer on a catchment scale: modeling and field studies. Hydrogeol. J. (submitted, under review).
A.R. Kacimov and M.M. Sherif. Sea water intrusion into a confined aquifer with controlled pumping: analytical solution. Water Resour. Res. (submitted, under review).
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Kacimov, A.R., Obnosov, Y.V., Sherif, M.M. et al. Analytical Solution to a Sea-water Intrusion Problem with a Fresh Water Zone Tapering to a Triple Point. J Eng Math 54, 197–210 (2006). https://doi.org/10.1007/s10665-006-9030-9
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DOI: https://doi.org/10.1007/s10665-006-9030-9