Nonpoint source pollution, space, time and asymetric information - a deposit refund approach

The incorporation of space allows the establishment of a more precise relationship between a contaminating input, a contaminating byproduct and emissions that reach the final receptor. However, the presence of asymmetric information impedes the implementation of the first-best policy. As a solution to this problem a site specific deposit refund system for the contaminating input and the contaminating byproduct are proposed. Moreover, the utilization of a successive optimization technique first over space and second over time enables definition of the optimal intertemporal site specific deposit refund system

Scale Effects in Hydraulic Model Tests of Rock Protected Structures, HR-119, 1970

A laboratory investigation was undertaken to determine the limiting model Reynolds number above which the scour behavior of rock protected structures can be reproduced in hydraulic models scaled according to the Froude criterion. A submerged jet was passed over an initially full scour pocket containing uniform glass spheres and the rate of scour was measured as a function of time. The dimensions of the scour pocket and jet and the particle diameters were varied as needed to maintain strict geometric similarity. For each of two different Froude numbers the Reynolds number was varied over a wide range. The normalized scour rate was found to be practically independent of the Reynolds number, R, (based on the jet velocity and particle diameter) at values of R above about 2.5 x 10^3, and to decrease with Rat smaller values. A grid placed in the jet was found to have a very strong effect on the scour rate. In an attempt to explain the effect of R on the scour behavior, turbulent pressure and velocity fluctuations were measured in air flows and water flows, respectively, over rigid scour pockets having the same geometry as those formed in the scour experiments. The normalized spectra of the fluctuations were found to be nearly independent of R, but the flow pattern was found to be very sensitive to the inlet condition, the jet deflecting upward or downward in a not wholly explainable manner. This indicates that scour behavior can be modeled only if the approach flow is also accurately modeled.

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.