Using the nonstationary spectral method to analyze asymptotic macrodispersion in uniformly recharged heterogeneous aquifers

SummaryThis paper describes an investigation of the influence of uniformly distributed groundwater recharge on asymptotic macrodispersion in two-dimensional heterogeneous media. This is performed using a nonstationary spectral approach [Li, S.-G., McLaughlin, D., 1991. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour. Res. 27 (7), 1589–1605; Li, S.-G., McLaughlin, D., 1995. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour. Res. 31 (3), 541–551] based on Fourier–Stieltjes representations for the perturbed quantities. To solve the problem analytically, focus is placed on the case where the local longitudinal dispersivity αL is much smaller than the integral scale of log transmissivity λ (i.e., αL/λ ≪ 1). The closed-form expressions are obtained for describing the spectrum of flow velocity, the variability of flow velocity and asymptotic macrodispersion, in terms of the statistical properties and the integral scale of log transmissivity, local transport parameters and a parameter β [Rubin, Y., Bellin, A., 1994. The effects of recharge on flow nonuniformity and macrodispersion. Water Resour. Res. 30 (4), 939–948] used to characterize the degree of flow nonuniformity due to the groundwater recharge. The impact of β on these results is examined.