Stochastic analysis of velocity spatial variability in bounded rectangular heterogeneous aquifers |
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| Affiliation: | 1. Department of Forest Engineering, Faculty of Forestry, Çankırı Karatekin University, 18200 Çankırı, Turkey;2. Department of Soil Science and Plant Nutrition, Faculty of Agriculture, Ordu University, 52250 Ordu, Turkey;3. Department of Field Crops, Faculty of Agriculture and Natural Sciences, Bilecik Seyh Edibali University, 11210 Gülümbe, Bilecik, Turkey;4. Department of Landscape Design and Architecture, Faculty of Forestry, Çankırı Karatekin University, 19200 Çankırı, Turkey;1. Department of Mathematics and Statistics, University of Nevada, Reno, Nevada 89557, USA;2. Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071, USA |
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| Abstract: | Transport of inert solutes in two-dimensional bounded heterogeneous porous media is investigated in a stochastic framework. After adopting a first-order approximation of the flow equations, analytical expressions are derived for the velocity covariances. Effects of the boundary conditions and aquifer size upon the statistical moments are analyzed. While the size of the domain is shown to have small influence on the covariances in most cases, the solutions are considerably modified by the boundaries. The results are compared with analytical solutions on infinite domains, and several discrepancies are demonstrated. For example, while the velocity variances on infinite domains are homogeneous, the present results are strongly non-stationary. Finally, the problem is solved numerically by the Monte Carlo simulation method. The results, including the behavior near the boundaries, are shown to be in close agreement with analytical solutions. |
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