2ND-ORDER EXPRESSIONS FOR VELOCITY MOMENTS IN 2-DIMENSIONAL AND 3-DIMENSIONAL STATISTICALLY ANISOTROPIC MEDIA

Second-order expressions are derived for the mean and covariance of st eady state seepage velocity under mean uniform flows in infinite two- and three-dimensional domains. The order of approximation is defined i n terms of the variance sigma(2) of a statistically homogeneous and an isotropic natural log hydraulic conductivity field Y with a Gaussian s patial autocorrelation function. Results show that second-order mean v elocity either exceeds or is dose to its first-order counterpart, depe nding on anisotropy. Head fluctuations of order larger than a affect s econd-order velocity moments to the same extent as do head fluctuation s of order a in virtually all cases, hence neglecting the former rende rs the results nonasymptotic. Velocity variances are generally larger when approximated 'consistently to second than to first order. The rat io between second- and first-order variance approximations is larger i n three than in two dimensions, larger for transverse than for longitu dinal velocity, and increases with sigma(2). Anisotropy has a signific ant effect on second-order velocity variance. Second-order effects hav e the greatest influence on longitudinal velocity variance at extreme anisotropy ratios and on transverse velocity variance in isotropic dom ains.