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Moving Boundaries in Earthscapes

Moving Boundaries in Earthscapes. Damien T. Kawakami, V.R. Voller, C. Paola, G. Parker, J. B. Swenson. NSF-STC www.nced.umn.edu. Badwater Deathvalley. Examples of Sediment Fans. 1km. How does sediment- basement interface evolve . An Ocean Basin

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Moving Boundaries in Earthscapes

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  1. Moving Boundaries in Earthscapes Damien T. Kawakami, V.R. Voller, C. Paola, G. Parker, J. B. Swenson NSF-STC www.nced.umn.edu

  2. Badwater Deathvalley Examples of Sediment Fans 1km How does sediment- basement interface evolve

  3. An Ocean Basin How does shoreline respond to changes in sea level and sediment flux

  4. Sediment transported and deposited over fan surface by fluvial processes From a momentum balance and drag law it can be shown that the diffusion coefficient n is a function of a drag coefficient and the bed shear stress t Sediment mass balance gives when flow is channelized n= cont. Convex shape when flow is “sheet flow” diffusion will be non-linear Conic shaped Fan A first order approx. analysis indicates n  1/r r radial distance from source

  5. An Ocean Basin How does shoreline respond to changes in sea level and sediment flux A large Scale Experiment by Paola and Parker at SAFL has addressed this problem

  6. “Jurassic Tank” ~1m Computer controlled subsidence

  7. How does shore line move in response to sea-level changes Swenson et al can be posed as a generalized Stefan Problem

  8. Numerical Solution 1-D finite difference deforming grid Base level (n calculated from 1st principles) Measured and Numerical results

  9. The Desert Fan Problem -- A 2D Problem A Stefan problem with zero Latent Heat

  10. A two-dimensional version (experiment) • Water tight basin filled with sand • First layer: gravel to allow easy drainage • Second layer: F110 sand with a slope ~5º. • Water and sand poured in corner plate • Sand type: Sil-Co-Sil at ~45 mm • Water feed rate: • ~460 cm3/min • Sediment feed rate: ~37 cm3/min

  11. The Numerical Method -Explicit, Fixed Grid, Up wind Finite Difference VOF like scheme The Toe Treatment fill point r P E Square grid placed on basement Flux out of toe elements =0 Until Sediment height > Downstream basement At end of each time step Redistribution scheme is required To ensure that no “downstream” covered areas are higher .05 grid size Determine height at fill Position of toe

  12. Experimental Measurements • Pictures taken every half hour • Toe front recorded • Peak height measure every half hour • Grid of squares • 10cm x 10cm

  13. Observations (1) • Topography • Conic rather than convex • Slope nearly linear across position and time • bell-curve shaped toe

  14. Observations (2) • Three regions of flow • Sheet flow • Large channel flow • Small channel flow • Continual bifurcation governed by shear stress

  15. Numerical results Constant diffusion model @ t=360min n= 4.7 • as a function of radius @ t=360min n=170/r, where r=[(iDx)2+(jDy)2]1/2 Diffusion chosen to match toe position

  16. Toe Position constant model

  17. Toe Position r model

  18. Constant r-model Non-Linear Diffusion model shows promise

  19. Moving Boundaries in Earthscapes A number of moving boundary problems in sedimentary geology have been identified. It has been shown that these problems can be posed as Generalized Stefan problems Fixed grid and deforming grid schemes have been shown to produce results in Reasonable agreement with experiments Improvements in model are needed Utilize full range of moving boundary numerical technologies to arrive at a suite of methods with geological application Use large scale general purpose solution packages

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