The stability of finite amplitude cellular convection and its relation to an extremum principle
Abstract
The stability of cellular convection flow in a layer heated from below is discussed for Rayleigh number R close to the critical value Rc. It is shown that in this region the stable stationary solution is determined by a minimum of the integral \[ \int_0^{H_0}R(H)\,dH, \] where R(H) is a functional of arbitrary convective velocity fields which satisfy the boundary conditions. For the stationary solutions R(H) is equal to the Rayleigh number. H0 is a given value of the convective heat transport. In a second part of the paper explicit results are derived for the convection problem with deviations from the Boussinesq approximation owing to the temperature dependence of the material properties.
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The conversion of heat into mechanical work by convective flow has not been discussed in detail in the literature of fluid dynamics, probably because the Boussinesq approximation corresponds to the limiting case when the conversion efficiency becomes vanishingly small.
“The conversion of heat into mechanical work by convective flow has not been discussed in detail in the literature of fluid dynamics, probably because the Boussinesq approximation corresponds to the limiting case when the conversion efficiency becomes vanishingly small (Malkus 1964; Busse 1967b).”
From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Busse 1967b
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Non-linear properties of thermal convection
Busse, F. H. (1978) · Reports on Progress in Physics · doi:10.1088/0034-4885/41/12/003 · Cited by 960 · see citing works
Self-citationMaximum entropy production principle in physics, chemistry and biology
Martyushev, L. M., & Seleznev, V. D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.12.001 · Cited by 943 · see citing works
Speculations on the Thermal and Tectonic History of the Earth
McKenzie, D., & Weiss, N. (2007) · Geophysical Journal of the Royal Astronomical Society · doi:10.1111/j.1365-246x.1975.tb05855.x · Cited by 335 · see citing works
Convection in an internally heated layer
Thirlby, R. (1970) · Journal of Fluid Mechanics · doi:10.1017/s0022112070002082 · Cited by 78 · see citing works
Stability of buoyancy-driven convection in a tilted slot
Liang, S. F., & Acrivos, A. (1970) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(70)90142-0 · Cited by 22 · see citing works
- Authors
- Busse, F. H.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Busse, F. H.
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 1967-12-22
- Volume
- 30
- Issue
- 4
- Pages
- 625-649
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W2167262170
- Cited by
- 547
- References
- 0
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 11 · 2023: 5 · 2022: 14 · 2021: 7 · 2020: 7 · 2019: 5 · 2018: 9 · 2017: 8 · 2016: 11 · 2015: 6 · 2014: 10 · 2013: 9 · 2012: 7
- FWCI
- 8.38
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Fluid Mechanics (publishedVersion)
- ERef Bayreuth (University of Bayreuth) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
- Physical Sciences › Engineering › Computational Mechanics › Fluid dynamics and aerodynamics studies
- Physical Sciences › Engineering › Computational Mechanics › Heat Transfer and Numerical Methods
- Keywords
- cellular convection, Rayleigh-Bénard convection, finite amplitude convection, stability, extremum principle, Rayleigh number, stationary solutions, convective heat transfer, Boussinesq approximation, temperature-dependent material properties, boundary layer
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