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An Eulerian scheme for the second‐order approximation of subsurface transport moments
Author(s) -
Naff R. L.
Publication year - 1994
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 - 10.1029/94wr00220
Subject(s) - mathematics , mathematical analysis , operator (biology) , exponential function , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
The moments of a conservative tracer cloud migrating in a mean uniform flow field are estimated using an operator approximation scheme; results are presented for the second, third, and fourth central moments in the mean flow direction. It is assumed that the spatially variable flow field, and therefore the tracer migration problem itself, is amenable to a probabilistic description; the effects of local dispersion on cloud migration are neglected in this study. Variation in the flow field is assumed to be the result of spatial variation in the hydraulic conductivity; spatial variation in porosity is assumed negligible. The operator approximation scheme, as implemented in this study, is second‐order correct, which requires a second‐order correct approximation of the velocity field correlation structure. Because estimation of the velocity correlation structure is decidedly the most difficult aspect of second‐order analysis, an ad hoc extension of the imperfectly stratified approximation developed earlier is implemented for this purpose. The first‐order approximation resulting from the operator expansion scheme is equivalent to small perturbation Eulerian results presented earlier (Naff, 1990, 1992). The infinite‐order approximation resulting from this scheme is equivalent to the exponential operator results obtained by Van Kampen (1976).