Introduction

This chapter presents a framework in which to understand the scale dependence and interaction of scales in large-scale models of conservative solute transport in groundwater. We are interested in models of conservative solute transport at practical field scales, on the order of a few meters to many kilometers. In particular, we examine how the dynamics on different scales are represented and interact in models developed using large-eddy-simulation (LES) methods from geophysical fluid dynamics (Rogallo and Moin, 1984). LES methods provide an ideal framework for our analysis because they allow us to define the scale of our model precisely.

This chapter presents a synthesis of findings from both groundwater hydrology and computational fluid dynamics. Our principal contribution will be to bring these two fields together in applications to groundwater problems. We shall first review the conceptual and technical basis for application of LES methods to conservative solute transport. We shall then examine the effects of advection and dispersion on the variability in the concentration field. We shall next investigate the effects of smaller-scale advection on the larger-scale component of the concentration field. We shall conclude with a brief and speculative analysis of strategies to incorporate the effects of unresolved, smaller-scale processes in larger-scale models of solute transport in groundwater.

Overview of LES

The roots of LES are in geophysical and engineering computational fluid dynamics, where many problems of interest involve turbulence (Rogallo and Moin, 1984). Turbulent velocity fields, governed by the Navier-Stokes equations, vary over a wide and continuous range of length and time scales.