On the Stability of Two‐Dimensional Convection in a Layer Heated from Below
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Longitudinal rolls are likely to be stabilized by shear and will not change to three-dimensional convection until the Rayleigh number considerably exceeds 22600.
“it appears likely that longitudinal rolls will be stabilized by the shear flow, and will not change to three-dimensional convection until the Rayleigk number considerably exceeds the value of 22 600 found for”
From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Busse (1967a)
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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
Oscillatory and collective instabilities in large Prandtl number convection
Busse, F. H., & Whitehead, J. A. (1974) · Journal of Fluid Mechanics · doi:10.1017/s0022112074000061 · Cited by 186 · see citing works
Self-citationScaling of plate-tectonic convection with pseudoplastic rheology
Korenaga, J. (2010) · Journal of Geophysical Research: Solid Earth · doi:10.1029/2010jb007670 · Cited by 89 · see citing works
“…dissipation, I defineΦc as the viscous335 dissipation within the region abovez∗ = c,336 Φc = ∫ c 0 ( ∫ η∗e∗i je ∗ i jdx ∗ ) dz∗, (31)337 and calculateΦδ , Φδ/2, andΦ (≡ Φ1), whereδ is (on average) the maximum thickness of the338 16 top thermal boundary layer [e.g.,Busse, 1967],339 δ = 2Nu−1.”
- Authors
- Busse, F. H.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Busse, F. H.
- ORCID
- Busse, F. H.
- Venue
- Journal of Mathematics and Physics
- Publisher
- Wiley
- Published
- 1967-04
- Volume
- 46
- Issue
- 1-4
- Pages
- 140-150
- ISSN
- 0022-2526 (ISSN-L)
- 0097-1421
- OpenAlex
- W159546068
- Cited by
- 291
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 4 · 2022: 3 · 2021: 6 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 5 · 2016: 3 · 2015: 3 · 2014: 2 · 2013: 4 · 2012: 2
- FWCI
- 7.61
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Studies in Applied Mathematics (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 › Mathematics › Applied Mathematics › Navier-Stokes equation solutions
- Keywords
- two-dimensional convection, Rayleigh-Bénard convection, stability analysis, heated fluid layer, thermal convection onset
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