Self-organized geodynamics of karst limestone landscapes and coupled terra rossa/bauxite formation

Why do flat limestones overlain by terra rossa or bauxite systematically adopt so-called karst geomorphology, which consists of sets of roughly regularly spaced wormholes, or funnels, or sinkholes, or tower karst? The idea that the funnels and sinkholes are located at the intersections of preexisting sets of subvertical fractures is untenable. New field and petrographic evidence (Merino & Banerjee, J. Geology, 2008) revealed that, rather than 'residual' or 'detrital' (the only options that have been on the table for decades), the terra rossa/bauxite clays and Al- and Fe-oxyhydroxides grow authigenically at the base of the terra rossa, replacing the underlying limestone at a generally downward-moving reaction front several centimeters thick. The clay-for-limestone replacement, which preserves solid volume (because it takes place by clay-growth-driven pressure solution of calcite), releases H+ ions. These dissolve more calcite, generating considerable leached porosity in a narrow zone that travels with the replacement front. We proposed (Merino & Banerjee, J. Geology, 2008) that the moving leached-porosity maximum created at the front could trigger the reactive-infiltration instability (Chadam et al, IMA J. Appl. Math., 1986), causing the replacement-and-leaching reaction front to become regularly fingered, with the fingers jumping in scale to funnels, these to sinks, and these, when deep enough and merged together laterally, to tower karst. This new geodynamics would account both for the world-wide association of terra rossa and bauxite with karst limestones, and for the stunning, self-organized geomorphology of karst itself. We are testing these ideas through linear stability analysis of a simplified reaction-transport system of equations and through numerical solution of the full non-linear system of reaction-transport equations applicable, including aqueous speciation. Preliminary calculations (Banerjee & Merino, J. Geology, 2011) suggest that the replacement-and-leaching front is self-accelerating. The linear stability analysis may help to delineate climatic and hydrologic conditions for the development of spatial patterns of karst landscape and to predict the spacing of the patterns.