Shallow Water equations for Non-Newtonian fluids |
| |
| Authors: | Enrique D Fernández-Nieto Pascal Noble Jean-Paul Vila |
| |
| Institution: | 1. School of Science, Kathmandu University, Dhulikhel, Kavre, Nepal;2. Department of Mathematics, Tri-Chandra Multiple Campus, Tribhuvan University, Kathmandu, Nepal;3. Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal;4. Austrian Research Center for Forests-BFW, Department of Natural Hazards, Rennweg 1, 6020 Innsbruck, Austria;5. Institute of Applied Geology, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria;6. Geomorphological Systems and Risk Research (ENGAGE), Department of Geography and Regional Research, University of Vienna, Universitaetsstrasse 7, 1010 Vienna, Austria;7. Department of Geophysics, Steinmann Institute, University of Bonn, Meckenheimer Allee 176, D-53115 Bonn, Germany;1. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;2. Department of Mechanical Engineering, Ohio University, Athens, OH 45701-2979, USA |
| |
| Abstract: | The purpose of this paper is to provide a consistent thin layer theory for some Non-Newtonian fluids that are incompressible and flowing down an inclined plane under the effect of gravity. We shall provide a better understanding of the derivation of Shallow Water models in the case of power-law fluids and Bingham fluids. The method is based on asymptotic expansions of solutions of the Cauchy Momentum equations in the Shallow Water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q. Such a method has been first introduced in the case of Newtonian fluids where the computations are proved to be rigorous (Vila, in preparation 20]; Bresch and Noble, 2007 9]) whereas the more complex case of arbitrary topography has been treated formally (Boutounet et al., 2008 5]). The well posedness of the free surface Cauchy Momentum equations for these Non-Newtonian fluids is still an open problem: the computations carried out here are only formal. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
