Similarity solutions for spreading of a two-dimensional non-Newtonian gravity current in a porous layer

详细信息	查看全文 | 推荐本文 |

• 作者：Vittorio Di Federico^a ; ^{vittorio.difederico@unibo.it} ; Renata Archetti^a ; ^{renata.archetti@unibo.it} ; Sandro Longo^b ; ^{sandro.longo@unipr.it}
• 关键词：Power-law ; Porous medium ; Gravity current ; Self-similar solution
• 刊名：Journal of Non-Newtonian Fluid Mechanics
• 出版年：2012
• 期刊代码：103_03770257
• 类别：et
• 出版时间：June, 2012
• 卷：177-178
• 期：Complete
• 页码：46-53
• 文件大小：991 K

摘要

We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by the release from a point source of a volume of fluid increasing with time like t^伪. The equation of motion for power-law fluids in porous media is a modified Darcy鈥檚 law taking into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance equation yields a nonlinear differential problem which admits a self-similar solution describing the shape of the current, which spreads like t^{(伪+n )/(2+n)}, generalizing earlier results for Newtonian fluids. For the particular values 伪 = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the numerical scheme is tested against the analytical solutions. Two additional analytical approximations, valid for any 伪, are presented. The space-time development of the gravity current is discussed for different flow behavior indexes.