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Deterministic and Stochastic Analyses of Dispersion in an Unbounded Stratified Porous Medium
Author(s) -
Güven Oktay,
Molz Fred J.
Publication year - 1986
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/wr022i011p01565
Subject(s) - stratification (seeds) , porous medium , mathematics , second moment of area , moment (physics) , dispersion (optics) , stratified flows , stratified flow , flow (mathematics) , scale (ratio) , stochastic modelling , statistical physics , mathematical analysis , mechanics , geology , statistics , turbulence , porosity , physics , geometry , geotechnical engineering , classical mechanics , seed dormancy , botany , germination , quantum mechanics , dormancy , optics , biology
The dispersion of a conservative solute released instantaneously from a finite or point source in an unbounded, nonrandom periodically stratified porous medium is examined theoretically by applying the moment method of R. Aris (1956) and P. G. Saffman (1962). The governing moment equations are derived for a general stratified medium and then applied to study the detailed time‐dependent variations of various low‐order spatial moments of the three‐dimensional concentration distribution in a particular periodic (sinusoidal) stratified medium, both for the general case when the mean flow direction is inclined to the stratification as well as for the special case of flow parallel to the stratification. The present results confirm the previous results of V. K. Gupta and K. N. Bhattacharya (1986) regarding the asymptotic (large‐time) large‐scale dispersion coefficients for such a periodic medium. The present results which are obtained through a deterministic analysis are compared also with the results which would be obtained by using the previous stochastic theories of G. Matheron and G. deMarsily (1980) and L. W. Gelhar et al. (1979). The comparison reveals several similarities as well as some important differences between the results of the deterministic and stochastic analyses.