1. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu 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 Geometry and Heat transfer Models of Shoreline movements 1 As always “-- the material presented should be approached with an open mind, studied carefully, and critically considered.” Cobb County Geogia

2. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Fans Toes Shoreline Two Problems of Interest

3. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu 1km Examples of Sediment Fans Moving Boundary How does sediment- basement interface evolve Badwater Deathvalley

4. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu sediment h(x,t) x = u(t) bed-rock ocean x shoreline x = s(t) land surface  

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

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

7. 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

8. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Base level Measured and Numerical results ( calculated from 1 st principles) 1-D finite difference deforming grid vs. experiment +Shoreline balance

9. 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 Depth at toe

10. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu h(x,y,t) bed-rock ocean y shoreline x = s(t) land surface  (x,y,t) A 2-D Front -Limit of Cliff face Shorefront But Account of Subsidence and relative ocean level Enthalpy Sol. x y Solve on fixed grid in plan view Track Boundary by calculating in each cell

11. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu  s(t)   Hinged subsidence

12. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu A 2-D problem Sediment input into an ocean with an evolving trench driven By hinged subsidence First look at case where Ocean is at constant depth NO TRENCH Then Look at case with Trench

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

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17. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu

18. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu With Trench

19. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu

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22. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu

23. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu No Trench Trench Plan view movement of fronts

24. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu s(t) R shoreline sea-level geometric – model of shoreline movement with changing sea level q=1 Assumption of rapid fluvial transport allow for a geometric balance NOTE: REVERSE of shoreline! u(t)

25. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu sediment Movement of sediment plug behind a dam Dam reservoir profile With sediment plug downstream of dam At time t = 0 water level in reservoir dropped at a Constant rate assume cliff face no flow in or out Describe movement of Sediment by Water depth

26. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Experiments by Chris Bromley, University of Nottingham Ekwha dam Oregon

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32. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu sediment 0.001 0.0025 0.005 Movement of toe Goes as t 2 Movement of sediment plug behind a dam drawdown rate

33. 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 Po Shoreline position is signature of channels

34. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu Shoreline Tracking Model has been Validated (Experiments) And a numerical method based on Heat Transfer concepts has been Verified. Enthalpy Sol. Will allow for a first cut simulation of how sea-level and subsidence Could effect the motion of shorelines Can be used to model short time systems Related to dam removal Space and time dependent latent heat Other Systems of interest

35. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu e.g. the Dessert Sediment Fan 1km How does sediment- basement interface evolve Badwater Deathvalley

36. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu An experiment Water tight basin -First layer: gravel to allow easy drainage -Second layer: F110 sand with a slope ~4º. Water and sand poured in corner plate Sand type: Sil-Co-Sil at ~45 mm Water feed rate: ~460 cm 3 /min Sediment feed rate: ~37cm 3 /min

37. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu The Desert Fan Problem A Stefan problem with zero Latent Heat

38. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu The Numerical Method -Explicit, Fixed Grid, Up wind Finite Difference VOF like scheme Flux out of toe elements =0 Until Sediment height > Downstream basement fill point PE The Toe Treatment Square grid placed on basement At end of each time step Redistribution scheme is required To ensure that no “downstream” covered areas are higher r Determine height at fill : Position of toe.05 grid size

39. National Center for Earth-surface Dynamics an NSF Science and Technology Center www.nced.umn.edu y –  (x,t) = 0 On toe height at input fan with time