Sharp global nonlinear stability for a fluid overlying a highly porous material

被引：18

作者：

Hill, Antony A. ^{[1
]}

Carr, Magda ^{[2
]}

机构：

[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

[2] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2010年 / 466卷 / 2113期

关键词：

superposed porous-fluid convection; temperature-dependent viscosity; energy method; HEAT-TRANSFER; CONVECTION; FLOW; LAYER; INTERFACE; LIQUID;

D O I：

10.1098/rspa.2009.0322

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the Navier-Stokes equations into a stability analysis, previous literature on fluid/porous thermal convection has modelled the fluid using the linear Stokes equations. This paper derives global stability for the full nonlinear system, by utilizing a model proposed by Ladyzhenskaya. The nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds.

引用

页码：127 / 140

页数：14

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