Application of a fractional advection‐dispersion equation

2000/02/01 by David A. Benson, Stephen W. Wheatcraft, Mark M. Meerschaert · 11 citations
Engineering · Environmental Science · Mathematics · #Advection #Convection–diffusion equation #Derivative (finance) #Dispersion (optics) #Fractional Differential Equations Solutions #Fractional calculus #Geometry #Groundwater flow and contamination studies #Heat and Mass Transfer in Porous Media #Mathematical analysis #Mathematics #Mechanics #Meteorology #Physics #Plume #Scaling #Skewness #Statistics #TRACER #Thermodynamics

paper · pdf · doi:10.1029/2000wr900031

openalex publication_date 2000/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A transport equation that uses fractional‐order dispersion derivatives has fundamental solutions that are Lévy's α‐stable densities. These densities represent plumes that spread proportional to time 1/α , have heavy tails, and incorporate any degree of skewness. The equation is parsimonious since the dispersion parameter is not a function of time or distance. The scaling behavior of plumes that undergo Lévy motion is accounted for by the fractional derivative. A laboratory tracer test is described by a dispersion term of order 1.55, while the Cape Cod bromide plume is modeled by an equation of order 1.65 to 1.8.

Citations

• Dispersion of soluble matter in solvent flowing slowly through a tube

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