The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
On the stability of steady finite amplitude convection
Abstract
The static state of a horizontal layer of fluid heated from below may become unstable. If the layer is infinitely large in horizontal extent, the Boussinesq equations admit many different steady solutions. A systematic method is presented here which yields the finite-amplitude steady solutions by means of successive approximations. It turns out that not every solution of the linear problem is an approximation to the non-linear problem, yet there are still an infinite number of finite amplitude solutions. A similar procedure has been applied to the stability problem for these steady finite amplitude solutions with the result that three-dimensional solutions are unstable but there is a class of two-dimensional flows which are stable. The problem has been treated for both rigid and free boundaries.
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Citations
Cites
Finite amplitude cellular convection
Malkus, W. V. R., & Veronis, G. (1958) · Journal of Fluid Mechanics · doi:10.1017/s0022112058000410 · Cited by 658
The heat transport and spectrum of thermal turbulence
Malkus, W. V. R. (1954) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1954.0197 · Cited by 643
On maintained convective motion in a fluid heated from below
Pellew, A., & Southwell, R. V. (1940) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1940.0092 · Cited by 484
On the tendency towards hexagonal cells in steady convection
Palm, E. (1960) · Journal of Fluid Mechanics · doi:10.1017/s0022112060000530 · Cited by 269
Discrete transitions in turbulent convection
Malkus, W. V. R. (1954) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1954.0196 · Cited by 259
Some Further Results on the Bénard Problem
Reid, W. H., & Harris, D. L. (1958) · The Physics of Fluids · doi:10.1063/1.1705871 · Cited by 148
The non-linear interaction of a finite number of disturbances to a layer of fluid heated from below
Segel, L. A. (1965) · Journal of Fluid Mechanics · doi:10.1017/s002211206500023x · Cited by 88
Contribution to the theory of cellular thermal convection
Palm, E., & Øiann, H. (1964) · Journal of Fluid Mechanics · doi:10.1017/s0022112064000775 · Cited by 32
Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
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
Self-citationThe stability of finite amplitude cellular convection and its relation to an extremum principle
Busse, F. H. (1967) · Journal of Fluid Mechanics · doi:10.1017/s0022112067001661 · Cited by 547
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 323
Self-citationOn the Stability of Two‐Dimensional Convection in a Layer Heated from Below
Busse, F. H. (1967) · Journal of Mathematics and Physics · doi:10.1002/sapm1967461140 · Cited by 291
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Metadata
- Authors
- Schlüter, A., Lortz, D., & Busse, F.
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 1965-09
- Volume
- 23
- Issue
- 1
- Pages
- 129-144
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W2158902697
- Cited by
- 678
- References
- 8
- FWCI
- 13.42
- Type
- journal article
- Language
- en
- Open access
- closed
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