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Discussion papers | Copyright
https://doi.org/10.5194/esurf-2018-68
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 29 Aug 2018

Research article | 29 Aug 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).

The rarefied (non-continuum) conditions of tracer particle transport in soils, with implications for assessing the intensity and depth dependence of mixing from geochronology

David Jon Furbish1,2, Rina Schumer3, and Amanda Keen-Zebert4 David Jon Furbish et al.
  • 1Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, Tennessee, USA
  • 2Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, Tennessee, USA
  • 3Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada, USA
  • 4Division of Earth and Ecosystem Sciences, Desert Research Institute, Reno, Nevada, USA

Abstract. We formulate tracer particle transport and mixing in soils due to disturbance driven particle motions in terms of the Fokker-Planck equation. The probabilistic basis of the formulation is suitable for rarefied particle conditions, and for parsing the mixing behavior of extensive and intensive properties belonging to the particles rather than to the bulk soil. The significance of the formulation is illustrated with the examples of vertical profiles of expected 10Be concentrations and particle OSL ages for the benchmark situation involving a one-dimensional mean upward soil motion with nominally steady surface erosion in the presence of either uniform or depth dependent particle mixing, and varying mixing intensity. The analysis, together with Eulerian-Lagrangian numerical simulations of tracer particle motions, highlight the significance of calculating ensemble expected values of extensive and intensive particle properties, including higher moments of particle OSL ages, rather than assuming de facto a continuum-like mixing behavior, with implications for field sampling and for describing the mixing behavior of other particle and soil properties. Profiles of expected 10Be concentrations and OSL ages systematically vary with mixing intensity as measured by a Peclet number involving the speed at which particles enter the soil, the soil thickness, and the particle diffusivity. Profiles associated with uniform mixing versus a linear decrease in mixing with depth are distinct for moderate mixing, but become similar with either weak mixing or strong mixing; uniform profiles do not necessarily imply uniform mixing.

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Short summary
We present in this mostly theoretical contribution a systematic treatment of tracer particle mixing in soils. We elaborate the consequences of rarefied (non-continuum) conditions of transport and mixing, and we augment this with numerical analyses that reveal important information not readily apparent in the analytical formulations, including an illustration of the variability in 10Be concentrations and OSL ages of individual particles in soils, with implications for interpreting field data.
We present in this mostly theoretical contribution a systematic treatment of tracer particle...
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