Measuring hydraulic permeability in a streambed using the packer test

Permeability of a streambed is an important factor regulating nutrient and oxygen availability for aquatic biota. In order to investigate the relationship, an accurate permeability should be measured. However, it is difficult to measure permeability in a coarse gravel bed using a conventional permeability test. Moreover, turbulent flow may occur in coarse bed material, and then deviations from Darcy's law do occur. Thus, permeability calculated following Darcy's law may be overestimated under turbulent flow conditions and should be corrected. The packer test can be used in highly permeable gravel beds. We developed a field method applicable to a gravel bed using the packer test and derived an equation adopting a law of turbulent flow to study the problems under any type of flow condition. The accuracy of the equation was examined using a laboratory flume with a gravel bed. The results suggested that permeability calculated from Hvorslev's equation is overestimated for turbulent flow. In contrast, our equation, developed here, could evaluate permeability accurately under any type of flow condition. Copyright © 2005 John Wiley & Sons, Ltd.     

Relativistic corrections to the multiple scattering effect on the Sunyaev–Zel'dovich effect in the isotropic approximation

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev–Zel'dovich effect for clusters of galaxies and include the multiple scattering effects in the isotropic approximation. We present the results of the calculations by the Fokker–Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of     the ratio of both the contributions is −0.2 per cent in the Wien region. In the Rayleigh–Jeans region the ratio is −0.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.