MOVING BOUNDARY PROBLEMS ON THE EARTHS SURFACE V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+

1. ~10mm Grain Growth in Metal Solidification From W.J. Boettinger National Center for Earth-surface Dynamics an NSF Science and Technology Center MOVING BOUNDARY PROBLEMS ON THE EARTHS SURFACE V.R. Voller+, J. B. Swenson*, W. Kim+ and C. Paola+ + National Center for Earth-surface Dynamics University of Minnesota, Minneapolis *Dept. Geological Sciences and Large Lake Observatory, University of Minnesota-Duluth ~10km “growth” of sediment delta into ocean Ganges-Brahmaputra Delta Commonality between solidification and ocean basin formation www.nced.umn.edu

2. Melting vs. Shoreline movement An Ocean Basin

3. Experimental validation of shoreline boundary condition ~3m

4. Calculated front velocity from exp. measurment of RHS measured Experimental validation of shoreline boundary condition Flux balance at shoreline eXperimental EarthScape facility (XES) Flux base subsidence slope

5. A Melting Problem driven by a fixed flux with SPACE DEPENDENT Latent Heat L = gs Enthalpy Sol. Limit Conditions: A Fixed Slope Ocean q=1 h a b similarity solution s(t) g = 0.5

6. A even more simple version Assume a “cliff” face at shoreline h h b a b s(t) s(t) Let diffusivity LARGE in analytical solution Can model 2-D problem like polymer filling From previous analytical Simple Geometry or A Further Limit Solution—No sediment storage in the fluvial domain

7. Note: Can be used to account for effects of channels Iteration can be written in the form of Lattice Boltzmann iterations Voller: To be published in JCP 2005 In One-D iterations could look like W P E AMonte-Carlo (lattice-Boltzmann) Polymer Filling Algorithm “Dump” total flux in “gate” cell and redistribute excess over amount requiredfor filling to neighboring cells in ratios proportional tocoefficients of the discretization of

8. Simulation of shoreline motion into a variable depth ocean with variable channelization High K(1) chanalized surface t=50 Low K(0.05) few channels

9. t=100

10. t=150

11. t=200

12. t=250

13. t=300

14. Shoreline position is signature of channels The Poe Models can predict stratigraphy “sand pockets” = OIL WHY Build a model

15. geometric – model of shoreline movement with changing sea level NOTE: REVERSE of shoreline! shoreline sea-level Further Work:--Include Ocean Level Rise q=1 z(t) s(t) s(t)