Nonsteady End Effects in Hele-Shaw Cells

Abstract

Two new results are presented on the development of convective flow in a finite Hele-Shaw cell. First, it is shown that within a certain range of Rayleigh numbers there exist three regions in the fluid layer: the center region having a steady flow and the two end regions exhibiting time-dependent flow. Second, in the two end regions each flow oscillation is always found to be monoperiodic and the two are not correlated. Transition to a more complicated oscillation is not observed, and the flow never becomes chaotic. The time-dependent flow regime is bounded at low and high Rayleigh number by transitions to steady-state flow.