TY - JOUR
T1 - Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag
AU - Rees, D A S
AU - Magyari, Eugen
N1 - This was published as part of a Special Issue on Convective Instabilities in Porous Media
PY - 2017/5/20
Y1 - 2017/5/20
N2 - Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4π^2. At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.
AB - Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4π^2. At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.
KW - convection; porous, instability, weakly nonlinear, viscous dissipation, form drag
UR - https://doi.org/10.3390/fluids2020027
UR - https://doi.org/10.3390/fluids2020027
U2 - 10.3390/fluids2020027
DO - 10.3390/fluids2020027
M3 - Article
SN - 2311-5521
VL - 2
JO - Fluids
JF - Fluids
IS - 2
M1 - 27
ER -