An analytical study is made of the onset of convection in a saturated porous medium occupying a two-dimensional enclosure of uniform height, but whose width is slowly varying in an arbitrary manner, or one of uniform width, but whose height is slowly varying in an arbitrary manner. It is found that the variation of width generally has a stabilizing effect, whereas variation of height generally has a destabilizing effect.

1.
Nield
,
D. A.
, and
Bejan
,
A.
, 2006,
Convection in Porous Media
,
3rd ed.
,
Springer
, New York.
2.
Lowell
,
R. P.
, 1980, “
Topographically Driven Subcritical Hydrothermal Convection in the Oceanic Crust
,”
Earth Planet. Sci. Lett.
0012-821X,
49
, pp.
21
28
.
3.
Hartline
,
B. K.
, and
Lister
,
C. R. B.
, 1981, “
Topographic Forcing of Supercritical Convection in a Porous Medium Such as the Ocean Crust
,”
Earth Planet. Sci. Lett.
0012-821X,
55
, pp.
75
86
.
4.
Finlayson
,
B. A.
, 1972,
The Method of Weighted Residuals and Variational Principles
,
Academic Press
, New York.
You do not currently have access to this content.