Exact energy stability of Bénard–Marangoni convection at infinite Prandtl number
File(s)
Accepted version
Author(s)
Fantuzzi, G
Wynn, A
Type
Journal Article
Abstract
Using the energy method we investigate the stability of pure conduction in Pearson’s model for Bénard–Marangoni convection in a layer of fluid at infinite Prandtl number. Upon extending the space of admissible perturbations to the conductive state, we find an exact solution to the energy stability variational problem for a range of thermal boundary conditions describing perfectly conducting, imperfectly conducting, and insulating boundaries. Our analysis extends and improves previous results, and shows that with the energy method global stability can be proven up to the linear instability threshold only when the top and bottom boundaries of the fluid layer are insulating. Contrary to the well-known Rayleigh–Bénard convection set-up, therefore, energy stability theory does not exclude the possibility of subcritical instabilities against finite-amplitude perturbations.
Date Issued
2017-06-01
Date Acceptance
2017-05-10
Citation
Journal of Fluid Mechanics, 2017, 822
ISSN
1469-7645
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Journal of Fluid Mechanics
Volume
822
Copyright Statement
© Cambridge University Press 2017. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
Marangoni convection
nonlinear instability
variational methods
VARIATIONAL BOUNDS
INCOMPRESSIBLE FLOWS
THERMOCAPILLARY INSTABILITIES
SURFACE TENSION
DISSIPATION
SQUARES
SUM
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published
Article Number
R1