National Center for Earth-surface Dynamics an NSF Science and Technology Center 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 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center Fans Toes Shoreline Two Problems of Interest

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

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

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

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

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

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

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center  s(t)   Hinged subsidence

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center With Trench

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center No Trench Trench Plan view movement of fronts

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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)

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center Experiments by Chris Bromley, University of Nottingham Ekwha dam Oregon

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center

National Center for Earth-surface Dynamics an NSF Science and Technology Center sediment Movement of toe Goes as t 2 Movement of sediment plug behind a dam drawdown rate

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

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

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

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

National Center for Earth-surface Dynamics an NSF Science and Technology Center The Desert Fan Problem A Stefan problem with zero Latent Heat

National Center for Earth-surface Dynamics an NSF Science and Technology Center 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

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