Transport in Porous Media 26: 109–119, 1997. 109 c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Vorticity in Three-Dimensionally Random Porous Media VIVEK KAPOOR School of Civil & Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, U.S.A. e-mail: vkapoor@ce.gatech.edu (Received: 26 March 1996) Abstract. The flow gradient tensor controls the rate of dissipation of concentration fluctuations due to local dispersion, and therefore determines the rate of dilution of solute in a spatially random flow field. Off-diagonal terms of the flow gradient tensor quantify the rotational characteristics of the flow. A leading order description of the vorticity 1 2 3 , of flow in a three-dimensionally random spatially correlated hydraulic conductivity field x is made by relating the vorticity spectrum to the spectrum of ln x . Distinct components of the vorticity are found to be linearly uncorrelated ( 0 ). The characteristic vorticity component in the bulk flow direction is zero 1 0 , and the characteristic vorticity in the transverse directions 2 3 are inversely proportional to the hydraulic conductivity microscales in the other transverse direction, as exhibited in a numerical calculation of the vorticity. Key words: vorticity, random porous media, microscales, spectral method, heterogeneity, random field, stochastic. 1. Relationship Between Spatial Gradients of Flows and Dilution The motivation for understanding the spatial gradients of flows in heterogeneous porous media, and the vorticity of flows, is their central role in controlling the rate at which local dispersion destroys concentration fluctuations in porous media. Therefore, before calculating the vorticity of flows in random hydraulic conductiv- ity fields, which is the purpose of this work, connections between flow strain rates and concentration fluctuations are shown in this section. Fluid flow in heterogeneous hydraulic conductivity fields has received atten- tion in recent times, in part because of the practical need to predict contaminant transport in aquifers. The Lagrangian integral scales of spatially heterogeneous flows are well known to determine solute spreading rates in the pure advection limit and approximate relationships between spreading rates, the hydraulic con- ductivity spectrum, and local dispersion (e.g., Gelhar and Axness, 1983; Deng and Cushman, 1993, etc.) have also been developed. This note documents properties of the vorticity of flows in spatially correlated, three-dimensional, saturated, random hydraulic conductivity fields. The existence of vorticity in heterogeneous porous media flows has been recognized before (Bear, 1972), and recently Sposito (1994) explored some