The generation of 2-D random velocity fields of groundwater flows via stream functions

This paper is a further development of former papers of the authors on the direct simulation of random velocity fields describing groundwater flow in aquifers of spatially variable, but stochastically homogeneous hydraulic conductivity. We use the so-called dual description of groundwater flow by means of stream functions. Further assumptions are therefore steady state flow, far boundaries and no sources and sinks. By a perturbation approach we get a first-order approximation of the spectra of the random stream function and the random velocity field. The generation of random velocity fields via stream functions is attractive because of its parsimony in the use of parameters. Only a scalar random field must be generated. Again we adopt Mikhailovʹs method of “partitioning and randomizing the spectrum” for the simulation of a homogeneous Gaussian field. We also tackle the problem of conditional simulation of random velocity fields honoring measured velocity values at several locations. The generation method is illustrated by a comparison of empirical and theoretical spectra.