1. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu 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 National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Ganges-Brahmaputra Delta “growth” of sediment delta into ocean Grain Growth in Metal Solidification From W.J. Boettinger  m  10km Commonality between solidification and ocean basin formation

2. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu An Ocean Basin Melting vs. Shoreline movement

3. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Experimental validation of shoreline boundary condition ~3m

4. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Experimental validation of shoreline boundary condition eXperimental EarthScape facility (XES) Flux balance at shoreline Flux base subsidence slope Calculated front velocity from exp. measurment of RHS measured

5. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Limit Conditions: A Fixed Slope Ocean q=1   s(t)  similarity solution  Enthalpy Sol. A Melting Problem driven by a fixed flux with SPACE DEPENDENT Latent Heat L =  s

6. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu A Further Limit Solution—No sediment storage in the fluvial domain   s(t)  Let diffusivity  LARGE in analytical solution From previous analytical or Simple Geometry  s(t)  A even more simple version Assume a “cliff” face at shoreline Can model 2-D problem like polymer filling

7. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu A Monte-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 Iteration can be written in the form of Lattice Boltzmann iterations Voller: To be published in JCP 2005 Note: Can be used to account for effects of channels PWEIn One-D iterations could look like

8. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu High K(1) chanalized surface Low K(0.05) few channels Simulation of shoreline motion into a variable depth ocean with variable channelization t=50

9. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu t=100

10. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu t=150

11. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu t=200

12. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu t=250

13. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu t=300

14. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu WHY Build a model Models can predict stratigraphy “sand pockets” = OIL The Poe Shoreline position is signature of channels

15. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu s(t) z(t) Further Work:--Include Ocean Level Rise shoreline sea-level geometric – model of shoreline movement with changing sea level NOTE: REVERSE of shoreline! q=1