Analytical and numerical solution of a generalized Stefan problem exhibiting two moving boundaries with application to ocean delta formation

J. Lorenzo-Trueba, V. R. Voller

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

A model associated with the formation of sedimentary ocean deltas is presented. This model is a generalized one-dimensional Stefan problem bounded by two moving boundaries, the shoreline and the alluvial-bedrock transition. The sediment transport is a non-linear diffusive process; the diffusivity modeled as a power law of the fluvial slope. Dimensional analysis shows that the first order behavior of the moving boundaries is determined by the dimensionless parameter 0 ≤ Ra b ≤ 1-the ratio of the fluvial slope to bedrock slope at the alluvial-bedrock transition. A similarity form of the governing equations is derived and a solution that tracks the boundaries obtained via the use of a numerical ODE solver; in the cases where the exponent θ in the diffusivity model is zero (linear diffusion) or infinite, closed from solutions are found. For the full range of the diffusivity exponents, 0 ≤ θ → ∞, the similarity solution shows that when Ra b < 0.4 there is no distinction in the predicted speeds of the moving boundaries. Further, within the range of physically meaningful values of the diffusivity exponent, i.e., 0 ≤ θ ∼ 2, reasonable agreement in predictions extents up to Ra b ∼ 0.7. In addition to the similarity solution a fixed grid enthalpy like solution is also proposed; predictions obtained with this solution closely match those obtained with the similarity solution.

Original languageEnglish
Pages (from-to)538-549
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume366
Issue number2
DOIs
StatePublished - 15 Jun 2010

Keywords

  • Dual moving boundaries
  • Enthalpy solution
  • Sediment delta
  • Similarity solution
  • Stefan problem

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