| Abstract: | The problem of large-scale ( pseudoturbulent ) motion of a fluid in a nonuniform porous medium was formulated in 1]. Since in practice the local porosity  (x) is unknown, it may be considered a continuous random point function. The difference of the local values of the porosity (x) from the mean value  for the medium as a whole leads to the occurrence of random pseudoturbulent motions of the filtering fluid, which are superposed on the mean filtration flow. The characteristics of the large-scale filtration motion in a medium with this sort of random porosity were considered in detail in 1], where the formal solution is presented for the resulting equations for two-point correlations, based on the use of considerations of spatial invariance. Also presented is a qualitative discussion of the effect of pseudoturbulence of the filtering medium on the transport processes in the medium.We note that the considered problem of pseudoturbulence of a filtering fluid in a nonuniform porous medium does not have anything in common with the statistical problem of the motion of small fluid elements in a broken porous space. The latter problem is interesting in connection with the analysis of the convective diffusion processes in a porous body (both uniform and nonuniform) and, beginning with 3], has been considered in several studies, including 2].In the present study we have used a method for solving the problem which is significantly different in comparison with that of 1], based on the representation of the variation of the local porosity from point to point as a random process with independent increments. This method has the advantage that it permits expressing the required correlation functions in the form of quadratures with arbitrary values of the characteristic parameters. In the following, for simplicity we consider the axisymmetric problem under the assumption that the two-point correlation of the deviations of the local values of the porosity from the mean are representable in the form of an isotropie Gaussian function of the distance between the points. The explicit expressions for the correlations are also written in some approximation and the physical consequences resulting from these assumptions are discussed. |
