Flow and solute transport in random cylinder arrays : a model for emergent aquatic plant canopies

Abstract

With wetlands constituting about 6% of earth's land surface, aquatic vegetation plays a significant role in defining mean flow patterns and in the transport of dissolved and particulate material in the environment. However, the dependence of the hydrodynamic and transport processes on fundamental properties of an aquatic plant canopy has not been investigated systematically over the wide range of conditions that are observed in the field. A laboratory investigation was conducted to describe flow and solute transport in idealized emergent plant canopies. This thesis presents laboratory measurements of the mean drag, turbulence structure and intensity, and lateral dispersion of passive solute in arrays of randomly-distributed cylinders, a model for emergent, rigid aquatic plants. Mean drag per cylinder length normalized by the mean interstitial fluid velocity and viscosity increases linearly with cylinder Reynolds number. In contrast to the dependence previously reported for sparse arrays at Reynolds numbers greater than 1000, the drag coefficient increases with increasing cylinder density in intermediate and high cylinder densities. In dense arrays, turbulent eddies are constrained by the interstitial pore size such that the integral length scale is equal to the mean surface-to-surface distance between a cylinder in the array and its nearest neighbor. The classic scale model for mean turbulence intensity, which is a function of the inertial contribution to the drag coefficient, the solid volume fraction, and the integral length scale of turbulence normalized by d, is then confirmed with our laboratory measurements. Our laboratory experiments demonstrate that Kyy/ (<u>d), the asymptotic (Fickian) lateral dispersion coefficient normalized by the mean interstitial fluid velocity and d, is independent of Reynolds number at sufficiently high Reynolds number.

(cont.) Although previous models predict that asymptotic lateral dispersion increases monotonically with cylinder density, laboratory measurements reveal that lateral dispersion at high Reynolds number exhibits three distinct regimes. In particular, an intermediate regime in which Kyy/ (<u>d) decreases with increasing cylinder density is observed. A scale model for turbulent diffusion is developed with the assumption that only turbulent eddies with integral length scale greater than d contribute significantly to net lateral dispersion. The observed dependence of asymptotic dispersion on cylinder density is accurately described by a linear superposition of this turbulent diffusion model and existing models for dispersion due to the spatially-heterogeneous velocity field that arises from the presence of the cylinders. Finally, laboratory measurements support the conjecture that Kyy/ (<u>d) is not strongly dependent on Reynolds number in dense arrays at any Red. However, the distance required to achieve asymptotic dispersion is shown to depend strongly on the Reynolds number.