TY - JOUR
T1 - Non-Boussinesq effects on transitions in Hele-Shaw convection
AU - Hwang, Shyh-Hong
AU - Chang, Hsueh Chia
PY - 1989/1/1
Y1 - 1989/1/1
N2 - Mode jumping between buoyancy-induced convection patterns in a slender Hele-Shaw cell (height > width) is studied with a center manifold projection technique at a critical aspect ratio, where both the single-roll and double-roll convection patterns destabilize simultaneously. In contradiction to some experimental observations, the Boussinesq model with insulated or isothermal side wall conditions indicates that the single-roll mode never surrenders its stability and yields to the double-roll mode as the Rayleigh number is increased. By adding the temperature dependence of fluid density and conductivity to the heat equation, it is shown that the single-roll mode can now undergo secondary bifurcations. Hysteretic jumps to the double-roll mode and smooth transitions to a mixed mode, and even to a time-periodic convection pattern, are then possible.
AB - Mode jumping between buoyancy-induced convection patterns in a slender Hele-Shaw cell (height > width) is studied with a center manifold projection technique at a critical aspect ratio, where both the single-roll and double-roll convection patterns destabilize simultaneously. In contradiction to some experimental observations, the Boussinesq model with insulated or isothermal side wall conditions indicates that the single-roll mode never surrenders its stability and yields to the double-roll mode as the Rayleigh number is increased. By adding the temperature dependence of fluid density and conductivity to the heat equation, it is shown that the single-roll mode can now undergo secondary bifurcations. Hysteretic jumps to the double-roll mode and smooth transitions to a mixed mode, and even to a time-periodic convection pattern, are then possible.
UR - http://www.scopus.com/inward/record.url?scp=36549096665&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36549096665&partnerID=8YFLogxK
U2 - 10.1063/1.857403
DO - 10.1063/1.857403
M3 - Article
AN - SCOPUS:36549096665
VL - 1
SP - 924
EP - 937
JO - Physics of fluids. A, Fluid dynamics
JF - Physics of fluids. A, Fluid dynamics
SN - 0899-8213
IS - 6
ER -