A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem
- 9 December 1985
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 402 (1823) , 257-283
- https://doi.org/10.1098/rspa.1985.0118
Abstract
This paper uses a novel 'generalized energy' to study the stabilizing effect of rotation in the Benard problem. The nonlinear stability boundary we find is in very close agreement with the experiments of Rossby (Rossby, H. T. J. Fluid Mech. 36, 309-335 (1969)), who predicts sub-critical instabilities for high Taylor numbers for fluids with Prandtl number greater than or equal to 1, such as water.Keywords
This publication has 22 references indexed in Scilit:
- Non-linear stability of the magnetic Bénard problem via a generalized energy methodArchive for Rational Mechanics and Analysis, 1985
- Exchange of stabilities, symmetry, and nonlinear stabilityArchive for Rational Mechanics and Analysis, 1985
- Local estimates and stability of viscous flows in an exterior domainArchive for Rational Mechanics and Analysis, 1983
- Nonlinear convection in a rotating layer: Amplitude expansions and normal formsGeophysical & Astrophysical Fluid Dynamics, 1983
- On the Possibility of Subcritical InstabilitiesPublished by Springer Nature ,1971
- Théorie non linéaire de la stabilité des ecoulements laminaires dans le cas de ≪l'echange des stabilités≫Archive for Rational Mechanics and Analysis, 1971
- On the principle of exchange of stabilitiesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1969
- On the stability of the Boussinesq equationsArchive for Rational Mechanics and Analysis, 1965
- The instability of a layer of fluid heated below and subject to Coriolis forces. IIProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1955
- The instability of a layer of fluid heated below and subject to Coriolis forcesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1953