TY - JOUR
T1 - The nonlinear interaction of convection modes in a box of a saturated porous medium
AU - Florio, B.J.
AU - Bassom, Andrew
AU - Fowkes, Neville
AU - Judd, Kevin
AU - Stemler, Thomas
PY - 2015
Y1 - 2015
N2 - © 2015 Elsevier B.V. All rights reserved. Abstract A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.
AB - © 2015 Elsevier B.V. All rights reserved. Abstract A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.
U2 - 10.1016/j.physd.2015.03.010
DO - 10.1016/j.physd.2015.03.010
M3 - Article
SN - 0167-2789
VL - 301-302
SP - 48
EP - 58
JO - Physica D-Nonlinear Phenomena
JF - Physica D-Nonlinear Phenomena
ER -