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Application of a fractional advection‐dispersion equation
Author(s) -
Benson David A.,
Wheatcraft Stephen W.,
Meerschaert Mark M.
Publication year - 2000
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2000wr900031
Subject(s) - dispersion (optics) , skewness , plume , advection , tracer , scaling , fractional calculus , derivative (finance) , mathematics , convection–diffusion equation , physics , mathematical analysis , mechanics , meteorology , thermodynamics , statistics , geometry , optics , nuclear physics , financial economics , economics
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.