Variable-density saturated flow with modified Darcy's law: The salt lake problem and circulation

Water Resources Research

Volumn 43, Issue 2, 2007, Pages

  Wooding, Robin A ^a  

^a CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; SEEPAGE;

CONVECTIVE PLUMES; DARCY'S LAW; DENSITY GRADIENT; SEEPAGE FLOW;

FLOW OF WATER;

BOUNDARY CONDITIONS; FLOW OF WATER; MATHEMATICAL MODELS; NUMERICAL METHODS; SEEPAGE;

DARCY LAW; FLOW VELOCITY; PEAK FLOW; PLUME; RAYLEIGH NUMBER; SALINE LAKE; SATURATION; SECONDARY FLOW; SEEPAGE; TWO-DIMENSIONAL MODELING; VECTOR; VELOCITY PROFILE;

EID: 33947722104     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2005WR004377     Document Type: Article

References (36)

1. Abramowitz, M., and I. A. Stegun (1965), Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 1046 pp., Dover, Mineola, N. Y.
2. Adams, J., P. Swarztrauber, and R. Sweet (1988), FISHPAK: A package of Fortran subprograms for the solution of separable elliptic partial differential equations, NCAR Appl. Software, Natl. Cent. for Atmos. Res., Boulder, Colo.
3. Arakawa, A. (1966), Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, part 1, J. Comput. Phys., 1, 119-143.
4. Batchelor, G. K. (1967), An Introduction to Fluid Mechanics, 615 pp., Cambridge Univ. Press, New York.
5. Boddington, T., P. Bray, and D. I. Harvey (1971), Thermal theory of spontaneous ignition: Criticality in bodies of arbitrary shape, Philos. Trans. R. Soc. London, Ser. A, 270, 467-506.
6. Carslaw, H. S., and J. C. Jaeger (1959), The Conduction of Heat in Solids, 2nd ed., Clarendon, Oxford, U. K.
7. Diersch, H.-J. G., and O. Kolditz (2002), Variable-density flow and transport in porous media: Approaches and challenges, Adv. Water Resour., 25, 899-944.
8. Duffy, C. J., and S. Al-Hassan (1988), Groundwater circulation in a closed desert basin: Topographic scaling and climatic forcing, Water Resour. Res., 24, 1675-1688.
9. Elder, J. W. (1967a), Steady free convection in a porous medium heated from below, J. Fluid Mech., 27, 29-48.
10. Elder, J. W. (1967b), Transient convection in a porous medium, J. Fluid Mech., 27, 609-623.
11. Erdelyi, A., W. Magnus, F. Oberhettinger, and F. G. Tricomi (1954), Tables of Integral Transforms, vol. 1, 391 pp., McGraw-Hill, New York.
12. Henry, H. R. (1964), Effects of dispersion on salt encroachment in coastal aquifers, U.S. Geol. Surv. Water Supply Pap., 1613-C, C71-C84.
13. Holst, P. H., and K. Aziz (1972), Transient three-dimensional natural convection in confined porous media, Int. J. Heat Mass Transfer, 15, 73-90.
14. Home, R. N. (1979), Three-dimensional natural convection in a confined porous medium heated from below, J. Fluid Mech., 92, 751-766.
15. Horne, R. N., and J.-P. Caltagirone (1980), On the evolution of thermal disturbances during natural convection in a porous medium, J. Fluid Mech., 100, 385-395.
16. Horne, R. N., and M. J. O'Sullivan (1974), Oscillatory convection in a porous medium heated from below, J. Fluid Mech., 66, 339-352.
17. Lamb, H. (1945), Hydrodynamics, 738 pp., Dover, Mineola, N. Y.
18. Lapwood, E. R. (1948), Convection of a fluid in a porous medium, Proc. Cambridge Philos. Soc., 44, 508-521.
19. Liu, X.-D. (1993), A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws, SIAM J. Numer. Anal., 30, 701-716.
20. Luz Neto, H., J. N. N. Quaresma, and R. M. Cotta (2002), Natural convection in three-dimensional porous cavities: Integral transform method, Int. J. Heat Mass Transfer, 45, 3013-3032.
21. Mangalis, V. (1965), Handbook of Series for Scientists and Engineers, 134 pp., Elsevier, New York.
22. Mazzia, A., L. Bergamaschi, and M. Putti (2001), On the reliability of numerical solutions of brine transport in groundwater: Analysis of infiltration from a salt lake, Transp. Porous Media, 43, 65-86.
23. Nield, D. A., and A. Bejan (1999), Convection in Porous Media, 2nd ed., 546 pp., Springer, New York.
24. Prasad, A., and C. T. Simmons (2003), Unstable density-driven flow in heterogeneous porous media: A stochastic study of the Elder [1967b] "short heater" problem, Water Resour. Res., 39(1), 1007, doi:10.1029/ 2002WR001290.
25. Putti, M., W. W.-G. Yeh, and W. A. Mulder (1990), A triangular finite volume approach with high-resolution upwind terms for the solution of groundwater transport equations, Water Resour. Res., 26, 2865-2880.
26. Simmons, C. T., K. A. Narayan, and R. A. Wooding (1999), On a test case for density-dependent groundwater flow and solute transport models: The salt lake problem, Water Resour. Res., 35, 3607-3620.
27. Swarztrauber, P. N., and R. A. Sweet (1979), Efficient Fortran subprograms for the solution of separable elliptic partial differential equations, ACM Trans. Math. Software, 5, 352-364.
28. Tabeling, P. (2002), Two-dimensional turbulence: A physicist approach, Phys. Rep., 362, 1-62.
29. van Duijn, C. J., L. A. Peletier, and R. J. Schotting (1993), On the analysis of brine transport in porous media, Eur. J. Appl. Math., 4, 271-302.
30. van Duijn, C. J., R. A. Wooding, and A. van der Ploeg (2001), Stability criteria for the boundary layer formed by throughflow at a horizontal surface of a porous medium: Extensive version, RANA Rep. 01-05, 55 pp., Eindhoven Univ. of Technol., Eindhoven, Netherlands.
31. Voss, C. I. (1984), SUTRA: A finite-element simulation model for saturated-unsaturated fluid density-dependent groundwater flow with energy transport or chemically reactive single-species solute transport, U.S. Geol. Surv. Water Resour. Invest. Rep., 84-4369, 1-409.
32. Voss, C. I., and W. R. Souza (1987), Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone, Water Resour. Res., 23, 1851-1866.
33. Watson, G. N. (1966), A Treatise on the Theory of Bessel Functions, 2nd ed., 804 pp., Cambridge Univ. Press, New York.
34. Wooding, R. A. (1960), Rayleigh instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 9, 183-192.
35. Wooding, R. A., S. W. Tyler, and I. White (1997a), Convection in ground-water below an evaporating salt lake: 1. Onset of instability, Water Resour. Res., 33, 1199-1217.
36. Wooding, R. A., S. W. Tyler, P. A. Anderson, and I. White (1997b), Convection in groundwater below an evaporating salt lake: 2. Evolution of fingers or plumes, Water Resour. Res., 33, 1219-1228.