The rarefied (non-continuum) conditions of tracer particle transport in soils, with implications for assessing the intensity and depth dependence of mixing from geochronology
<p>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 intensi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2018-12-01
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| Series: | Earth Surface Dynamics |
| Online Access: | https://www.earth-surf-dynam.net/6/1169/2018/esurf-6-1169-2018.pdf |
| Summary: | <p>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 beryllium-10 (<span class="inline-formula"><sup>10</sup>Be</span>) concentrations and
optically stimulated luminescence (OSL) particle 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,
highlights 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. The analysis and results offer guidance for field sampling and for
describing the mixing behavior of other particle and soil properties.
Profiles of expected <span class="inline-formula"><sup>10</sup>Be</span> concentrations and OSL ages
systematically vary with mixing intensity as measured by a Péclet 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
they become similar with either weak mixing or strong mixing; uniform
profiles do not necessarily imply uniform mixing.</p> |
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| ISSN: | 2196-6311 2196-632X |