Jj. Wylie et Jr. Lister, THE EFFECTS OF TEMPERATURE-DEPENDENT VISCOSITY ON FLOW IN A COOLED CHANNEL WITH APPLICATION TO BASALTIC FISSURE ERUPTIONS, Journal of Fluid Mechanics, 305, 1995, pp. 239-261
A theoretical description is given of pressure-driven viscous flow of
an initially hot fluid through a planar channel with cold walls. The v
iscosity of the fluid is assumed to be a function only of its temperat
ure. If the viscosity variations caused by the cooling of the fluid ar
e sufficiently large then the relationship between the pressure drop a
nd the flow rate is non-monotonic and there can be more than one stead
y flow for a given pressure drop. The linear stability of steady flows
to two-dimensional and three-dimensional disturbances is calculated.
The region of instability to two-dimensional disturbances corresponds
exactly to those flows in which an increase in flow rate leads to a de
crease in pressure drop. At higher viscosity contrasts some flows are
most unstable to three-dimensional (fingering) instabilities analogous
, but not identical, to Saffman-Taylor fingering. A cross-channel-aver
aged model is derived and used to investigate the finite-amplitude evo
lution.