HR: 1340h
AN: NG33C-0187    [Abstracts]
TI: Stalactite Growth as a Free-Boundary Problem
AU: * Goldstein, R E
EM: gold@physics.arizona.edu
AF: University of Arizona, Department of Physics and Program in Applied Mathematics 1118 E. 4th St., Tucson, AZ 85721 United States
AU: Short, M B
EM: mshort@physics.arizona.edu
AF: University of Arizona, Department of Physics 1118 E. 4th St., Tucson, AZ 85721 United States
AU: Baygents, J C
EM: jcb@maxwell.che.arizona.edu
AF: University of Arizona, Department of Chemical and Environmental Engineering, Tucson, AZ 85721 United States
AB: The chemical mechanisms underlying the growth of speleothems are well known, but no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. We consider^1,2 the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and carbon dioxide transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites. Generalizations of this analysis to study the linear instability leading to crenulations are discussed. This work lays the foundation for a systematic study of speleothem morphologies and isotopic distributions therein. ¹M.B. Short, J.C. Baygents, J.W. Beck, D.A. Stone, R.S. Toomey, III, and R.E. Goldstein, Phys. Rev. Lett. 94, 018501 (2005); ² M.B. Short, J.C. Baygents, and R.E. Goldstein, Phys. Fluids 17, 083101 (2005). Supported by NSF ITR Grant PHY0219411
DE: 1854 Precipitation (3354)
DE: 3200 MATHEMATICAL GEOPHYSICS (0500, 4400, 7833)
DE: 4460 Pattern formation
DE: 4958 Speleothems
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005