Analytical Solution for Anomalous Diffusion of Bedload Tracers Gradually Undergoing Burial

Zi Wu, Efi Foufoula-Georgiou, Gary Parker, Arvind Singh, Xudong Fu, Guangqian Wang

Research output: Contribution to journalArticle

Abstract

Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2-D Exner-Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection-diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion-induced scaling (∝t 1 ) and an advection-induced scaling (∝t 3 ) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations.

Original languageEnglish (US)
Pages (from-to)21-37
Number of pages17
JournalJournal of Geophysical Research: Earth Surface
Volume124
Issue number1
DOIs
StatePublished - Jan 1 2019

Fingerprint

bedload
tracers
tracer techniques
tracer
Advection
Substrates
active layer
Rivers
advection
timescale
formulations
substrate
Computer simulation
advection-diffusion equation
scaling
sinks
rivers
preserves

Keywords

  • anomalous diffusion
  • bedload transport
  • tracer burial

ASJC Scopus subject areas

  • Geophysics
  • Forestry
  • Oceanography
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Palaeontology

Cite this

Analytical Solution for Anomalous Diffusion of Bedload Tracers Gradually Undergoing Burial. / Wu, Zi; Foufoula-Georgiou, Efi; Parker, Gary; Singh, Arvind; Fu, Xudong; Wang, Guangqian.

In: Journal of Geophysical Research: Earth Surface, Vol. 124, No. 1, 01.01.2019, p. 21-37.

Research output: Contribution to journalArticle

Wu, Zi ; Foufoula-Georgiou, Efi ; Parker, Gary ; Singh, Arvind ; Fu, Xudong ; Wang, Guangqian. / Analytical Solution for Anomalous Diffusion of Bedload Tracers Gradually Undergoing Burial. In: Journal of Geophysical Research: Earth Surface. 2019 ; Vol. 124, No. 1. pp. 21-37.
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