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<article language="en">
	<journal>
		<journal_title>Hydrology and Earth System Sciences</journal_title>
		<journal_url>www.hydrol-earth-syst-sci.net</journal_url>
		<issn>1027-5606</issn>
		<eissn>1607-7938</eissn>
		<volume_number>12</volume_number>
		<issue_number>6</issue_number>
		<publication_year>2008</publication_year>
	</journal>
	<doi>10.5194/hess-12-1285-2008</doi>
	<article_url>http://www.hydrol-earth-syst-sci.net/12/1285/2008/</article_url>
	<abstract_html>http://www.hydrol-earth-syst-sci.net/12/1285/2008/hess-12-1285-2008.html</abstract_html>
	<fulltext_pdf>http://www.hydrol-earth-syst-sci.net/12/1285/2008/hess-12-1285-2008.pdf</fulltext_pdf>
	<start_page>1285</start_page>
	<end_page>1293</end_page>
	<publication_date>2008-12-01</publication_date>
	<article_title content_type="html">Infiltrative instability near topography with implication for the drainage of soluble rocks</article_title>
	<authors>
		<author numeration="1" affiliations="1">
			<name>P. Genthon</name>
			<email>pierre.genthon@ird.ne</email>
		</author>
		<author numeration="2" affiliations="2,3">
			<name>A. Ormond</name>
		</author>
	</authors>
	<affiliations>
		<affiliation numeration="1" content_type="html">Paléotropique, IRD, BP A5 98848 Nouméa, New Caledonia</affiliation>
		<affiliation numeration="2" content_type="html">DTP, Obs. Midi Pyrénées, Toulouse, France</affiliation>
		<affiliation numeration="3" content_type="html">now at: HydroSciences, IRD BP11416 Niamey, Niger</affiliation>
	</affiliations>
	<abstract content_type="html">We present here numerical modeling of infiltration instability near a
topographic edge of a water-saturated porous slice by analogy with a
limestone formation devoid of initial heterogeneities such as fractures
faults or joints and limited by a vertical cliff. In our runs a first
dissolution finger develops near the cliff edge, and ends to intersect it
above its mid height. Additional fingers develop upstream with a decreasing
growth rate and an increasing width. This results from the decrease of the
infiltration velocity with distance to the cliff in our models. A
sensitivity study shows that a larger permeability contrast between the
fingers and the initial undissolved porous medium produces a larger number
of fingers, while increasing the dispersivity (lower Peclet number) produces
wider fingers. A slower reaction rate (lower Damkhöler number) produces
fingers that follow the initial flow lines, since dissolution occurs
simultaneously along the entire finger. These results suggest that
alteration by dissolution of limestones or other soluble formations may
produce different underground channel structures in the same drainage basin
due to local changes of the non-dimensional &lt;i&gt;Pe&lt;/i&gt; and &lt;i&gt;Da&lt;/i&gt; numbers.</abstract>
	<references>
		<reference numeration="1" content_type="text">Bekri, S., Thovert, J. F., and Adler, P. M.: Dissolution of porous media, Chem. Eng. Sci., 50, 2765–2791, 1995. </reference>
		<reference numeration="2" content_type="text">Dreybrodt, W.: Principles of early development of karst conduits under natural and man-made condition revealed by mathematical analysis of numerical models, Water Resour. Res., 32, 2923–2935, 1996. </reference>
		<reference numeration="3" content_type="text">Daccord, G. and Lenormand, R.: Fractal patterns from chemical dissolution, Nature, 325, 41–43, 1987. </reference>
		<reference numeration="4" content_type="text">Ford, D. C. and Williams, P. W.: Karst geomorphology and hydrology, Chapman and Hall, London, 601 pp., 1994. </reference>
		<reference numeration="5" content_type="text">Fredd, C. N. and Fogler, H. S.: Influence of transport and reaction on wormhhole ormation in porous media, AIChE J., 44, 1933–1949, 1998. </reference>
		<reference numeration="6" content_type="text">Gelhar, L. W., Welty, C., and Rehfeldt, K. R.: A critical review of data on field-scale dispersion in aquifers, Wat. Resour. Res., 28, 1955–1974, 1992. </reference>
		<reference numeration="7" content_type="text">Gabrovsek, F. and Dreybrodt, W.: A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth, J. Hydrol., 240, 206–224, 2001. </reference>
		<reference numeration="8" content_type="text">Gabrovsek, F., Romanov, D., and Dreybrodt, W.: Early karstification in a dual-fracture aquifer: the role of exchange of flow between prominent fractures and a dense net of fissures, J. Hydrol., 299, 45–66, 2004. </reference>
		<reference numeration="9" content_type="text">Golfier, F., Zarcone, C., Bazin, B., Lenormand, R., Lasseux, D., and Quintard, M.: On the ability of Darcy-scale models to capture wormhole formation during the dissolution of a porous medium, J. Fluid Mech., 457, 213–254, 2002. </reference>
		<reference numeration="10" content_type="text">Hackbusch, W.: Multi-grid methods and applications, Springer Verlag, New York, 1985. </reference>
		<reference numeration="11" content_type="text">Hirt, C. W. and Nichols, B. D.: Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201–225, 1981. </reference>
		<reference numeration="12" content_type="text">Kaufmann, G.: Modelling unsaturated flow in an evolving karst aquifer, J. Hydrol., 276, 53–70, 2003. </reference>
		<reference numeration="13" content_type="text">Kaufmann, G. and Braun, J.: Karst aquifer evolution in fractured rocks, Water Resour. Res., 35, 3223–3228, 1999. </reference>
		<reference numeration="14" content_type="text">Kaufmann, G. and Braun, J.: Karst aquifer evolution in fractured, porous rocks, Water Resour. Res., 36, 1381–1391, 2000. </reference>
		<reference numeration="15" content_type="text">Lichtner, P. C.: The quasi-stationnary state approximation to coupled mass transport and fluid/rock reaction in a porous media, Geochim. Cosmochim. Acta, 52, 143–165, 1988. </reference>
		<reference numeration="16" content_type="text">Lowry, T. and Li, S.: A characteristic-based finite analytic method for solving the two-dimensional steady state advection-diffusion equation, Water Ressour. Res., 38(7), 1123, doi:10.1029/2001WR000518, 2002. </reference>
		<reference numeration="17" content_type="text">Mangin, A.: Karst hydrogeology, in: Groundwater Ecology, edited by: Gilbert, J., Danielopol, D. L., Stanford, J., and Thorp, J. H., Academic Press, New York, 1995. </reference>
		<reference numeration="18" content_type="text">Ogata, A.: Mathematics of dispersion with linear absorbtion isotherm, US Geol. Surv. Prof. Paper, 411-H, 9 pp., 1964. </reference>
		<reference numeration="19" content_type="text">Ogata, A.: Therory of dispersion in granular medium, US Geol. Surv. Prof. Paper, 411-I, 34 pp., 1970. </reference>
		<reference numeration="20" content_type="text">Ortoleva, P. J., Chadam, J., Merino, E., and Sen, A.: Geochemical self-organization II, The reactive infiltration instability, Am. J. Sci., 287, 1008–1040, 1987. </reference>
		<reference numeration="21" content_type="text">Ormond, A. and Ortoleva, P. J.: Numerical modelling of reaction-induced cavities in porous rock, J. Geophys. Res., 105, 16 737–16 747, 2000. </reference>
		<reference numeration="22" content_type="text">Palmer, A. N.: Origin and morphology of limestone caves, Geol. Soc. Am. Bull., 103, 1–21, 1991. </reference>
		<reference numeration="23" content_type="text">Quintard, M. and Whitaker, S.: Dissolution of an immobile phase during flow in porous media, Ind. Eng. Chem. Res., 38, 833–844, 1999. </reference>
		<reference numeration="24" content_type="text">Siemers, J. and Dreybordt, W.: Early development of karst aquifers on percolation networks of fractures in limestone, Water Resour. Res., 34, 409–419, 1998. </reference>
		<reference numeration="25" content_type="text">Steefel, C. I. and Lasaga, A. C: Evolution of dissolution patterns: permeability changes due to coupled flow and reaction, in: Chemical Modelling of Aqueous Systems II, edited by: Melchior, D. C. and Bassett, R. L., Am. Chem. Soc. Symp. Ser., 416, 212–225, 1990. </reference>
		<reference numeration="26" content_type="text">Steefel, C. I. and Lasaga, A. C.: Putting transport into water-rock interaction models, Geology, 20, 680–684, 1992. </reference>
		<reference numeration="27" content_type="text">Trescases, J. J.: L&apos;evolution géochimique supergène des roches ultrabasiques en zone tropicale: formation des gisements nickelifères de Nouvelle Calédonie, Mem. Orstom, 78, 259 pp., 1975. </reference>
		<reference numeration="28" content_type="text">Willems, L., Pouclet, A., and Vicat, J. P.: Existence de karst en roches cristallines silicatées non carbonatées en Afrique Sahélienne et équatoriale, implications hydrogéologiques, Bull. Soc. Geol. Fr., 173, 337–345, 2002. </reference>
		<reference numeration="29" content_type="text">Wray, R. A. L.: A global review of solutional weathering forms on quartz sanstones, Earth Sci. Rev., 42, 137–160, 1997. </reference>
	</references>
</article>

