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The Diffusion of Passive Tracers in Laminar Shear Flow
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Longitudinal dispersivity data and implications for scaling behavior.

Dirk Schulze-Makuch1

  • 1Department of Geology, Washington State University, Webster Physical Sciences Building, Pullman, WA 99164, USA. dirksm@wsu.edu

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Summary
This summary is machine-generated.

Longitudinal dispersivity data from 109 authors reveal a power-law relationship with scale. The scaling exponent, close to 0.5 for reliable data, shows no significant difference across geological media types.

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Area of Science:

  • Hydrogeology
  • Geosciences
  • Environmental Engineering

Background:

  • Longitudinal dispersivity (alpha) is a critical parameter in groundwater flow and contaminant transport modeling.
  • Existing data on dispersivity across various geological media are fragmented and require synthesis for broader application.
  • Understanding the scale dependency of dispersivity is crucial for accurate predictions in heterogeneous subsurface environments.

Purpose of the Study:

  • To compile and analyze a comprehensive dataset of longitudinal dispersivity from diverse geological media.
  • To investigate the relationship between longitudinal dispersivity and the scale of measurement.
  • To provide a preliminary guide for groundwater practitioners and to inform theories on scaling behavior.

Main Methods:

  • Compilation of longitudinal dispersivity (alpha) data from 109 authors across various geological media.
  • Subdivision of data into consolidated (basalts, granites, sandstones, carbonates) and unconsolidated media subsets.
  • Statistical analysis to determine the empirical relationship between dispersivity and scale, identifying scaling exponents.

Main Results:

  • A power-law relationship empirically best describes dispersivity as a function of measurement scale.
  • Scaling exponents for consolidated and unconsolidated media range from 0.40-0.92 and 0.44-0.94, respectively.
  • Higher reliability data suggest scaling exponents are closer to 0.5, with no significant differences observed among media types.

Conclusions:

  • Longitudinal dispersivity exhibits scale-dependent behavior best modeled by a power law across different geological formations.
  • The scaling exponent is consistently around 0.5 for high-quality data, indicating a universal scaling behavior.
  • No evidence supports an upper bound or asymptotic behavior in the dispersivity-scale relationship for the analyzed media.