Oscillatory and collective instabilities in large Prandtl number convection
Abstract
An experimental study of transitions from steady bimodal convection to time-dependent forms of convection is described. Using controlled initial conditions for the onset of bimodal convection two mechanisms of instability can be separated from the effects of random noise. The oscillatory instability of bimodal cells introduces standing waves closely resembling those occurring in low Prandtl number convection. The collective instability introduces spoke-pattern convection which is characteristic for turbulent large Prandtl number convection. Both instabilities originate primarily from the momentum advection terms in the equations of motion, as is evident from the strong Prandtl number dependence of the critical Rayleigh number Rt for the onset of oscillations. The results are discussed in relation to previous experiments and recent theoretical work.
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In those experiments, the formation of two scales with time-dependence occurred because momentum was advected.
“the formation of two scales, with time-dependence of the resulting flow, occurred because momentum was advected.”
From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Busse & Whitehead (1974)
In laboratory studies of Rayleigh-Benard convection, Busse & Whitehead (1974) and Busse (private communication) demonstrated that two scales of flow occur when the Rayleigh number exceeds 2.4 x 10^5.
“In laboratory studies of Rayleigh-BCnard convection Busse & Whitehead (1974) and Busse (private communication) have demonstrated that two scales of flow occur when the Rayleigh number exceeds 2 .4 ~ lo5.”
From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Busse & Whitehead (1974)
Cites
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Transition to time-dependent convection
Clever, R. M., & Busse, F. H. (1974) · Journal of Fluid Mechanics · doi:10.1017/s0022112074001571 · Cited by 461 · see citing works
Self-citationInstabilities of convection rolls in a high Prandtl number fluid
Busse, F. H., & Whitehead, J. A. (1971) · Journal of Fluid Mechanics · doi:10.1017/s0022112071001071 · Cited by 327 · see citing works
Self-citationKrishnamurti, R. (1970) · Journal of Fluid Mechanics · doi:10.1017/s0022112070001271 · Cited by 322 · see citing works
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Busse, F. H. (1967) · Journal of Mathematics and Physics · doi:10.1002/sapm1967461140 · Cited by 291 · see citing works
Self-citationSome further studies on the transition to turbulent convection
Krishnamurti, R. (1973) · Journal of Fluid Mechanics · doi:10.1017/s0022112073000170 · Cited by 274 · see citing works
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Busse, F. H. (1972) · Journal of Fluid Mechanics · doi:10.1017/s0022112072002988 · Cited by 252 · see citing works
Self-citationOn the transition to turbulent convection. Part 2. The transition to time-dependent flow
Krishnamurti, R. (1970) · Journal of Fluid Mechanics · doi:10.1017/s0022112070001283 · Cited by 249 · see citing works
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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-citationSpeculations 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
- Authors
- Busse, F. H., & Whitehead, J. A.
- Affiliations
- University of California, Los Angeles (US)
- ORCID
- Whitehead, J. A.
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 1974-10-21
- Volume
- 66
- Issue
- 1
- Pages
- 67-79
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W2071228004
- Cited by
- 186
- References
- 13
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 1 · 2020: 5 · 2019: 1 · 2018: 1 · 2017: 2 · 2014: 5 · 2013: 1 · 2012: 2
- FWCI
- 18.02
- 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 › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Engineering › Computational Mechanics › Combustion and flame dynamics
- Keywords
- oscillatory instability, collective instabilities, standing waves, momentum advection, critical Rayleigh number, Rayleigh-Bénard convection
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