The flow field at the vicinity of porous media surfaces
A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. We show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained
Shavit, U., Bar-Yosef, G., Rosenzweig, R., and Assouline, S., Modified Brinkman Equation for a Free Flow Problem at the Interface of Porous Surfaces: The Cantor- Taylor Brush Configuration Case. Water Resources Research, 38(12), 1320-1334, 2002 (pdf).
Shavit, U., Rosenzweig, R., and Assouline, S., Free Flow at the Interface of Porous Surfaces: Generalization of the Taylor Brush Configuration. Transport in Porous Media, in press (pdf).
Rosenzweig, R. and Shavit, U., The laminar flow field at the interface of a Sierpinski carpet configuration, Water Resources Research (pdf).
Dispersion of tracers in a flume with emergent vegetation
The mixing of pollutants in natural and constructed systems such as wetlands and streams received in recent years a renewed attention. The flow in such systems passes in-between solid obstacles such as stems and vegetation branches. In such cases, local geometry variations play the most important role in affecting both flow and transport. Accurate modeling of pollutant transport in streams, wetlands and other regions of open water flow involving vegetation is crucial for keeping these environments clean and healthy.
Dispersion is a macro-scale representation of local, micro-scale, transport mechanisms. It is the most important spreading process but the most difficult to model. The detailed micro-scale geometry and the subsequent complex local velocity field are typically unavailable. Even when the detailed geometry is known, modeling of the fluid mechanics is nearly impossible due to the wide range of scales. In practice, flow rate, stem diameter, and vegetation density can only be estimated.