THE EFFECTS OF TEMPERATURE-DEPENDENT VISCOSITY ON FLOW IN A COOLED CHANNEL WITH APPLICATION TO BASALTIC FISSURE ERUPTIONS

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.