Natural convection in a long vertical cylinder under gravity modulation
- 1 August 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 193 (-1) , 391-415
- https://doi.org/10.1017/s0022112088002198
Abstract
This study is devoted to the onset of convection in differentially heated cylinders under gravity modulation. It specifically concerns the case of a vertical cylinder of infinite length, when a negative temperature gradient is maintained in the upward direction. The effect of modulation on the stability limits given by linear theory in the standard steady case is analysed. A method based on Floquet theory is proposed in the case of small values of the modulation amplitude ε, for a fixed value of the frequency ω. A general technique, called matrix method, which can easily be adapted to various kinds of geometries and boundary conditions, has been developed. Analytical approaches have been derived in some cases. Finally, an asymptotic analysis is presented for large ω, under very general boundary conditions and periodic constraints, for finite ε. An asymptotic relation is established for the onset of convection under periodic gravity modulation for large ω values, when ε [Lt ] ω; the mathematical and physical foundations of this inequality are discussed.Keywords
This publication has 17 references indexed in Scilit:
- Low-Gravity Fluid FlowsAnnual Review of Fluid Mechanics, 1982
- The stability of unsteady cylinder flowsJournal of Fluid Mechanics, 1975
- Global stability of time-dependent flows. Part 2. Modulated fluid layersJournal of Fluid Mechanics, 1974
- Instability of unsteady flows or configurations. Part 2. Convective instabilityJournal of Fluid Mechanics, 1972
- On thermoconvective instability in a bounded cylindrical fluid layerInternational Journal of Heat and Mass Transfer, 1971
- On convective stability in the presence of periodically varying parameter: PMM vol. 34, n≗3, 1970, pp. 470–480Journal of Applied Mathematics and Mechanics, 1970
- Thermoconvective instability in a bounded cylindrical fluid layerInternational Journal of Heat and Mass Transfer, 1970
- The effects of gravity modulation on the stability of a heated fluid layerJournal of Fluid Mechanics, 1970
- The stability of steady and time-dependent plane Poiseuille flowJournal of Fluid Mechanics, 1968
- On parametric excitation of convective instabilityJournal of Applied Mathematics and Mechanics, 1963