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Cited by 70Fluid Dynamics and Turbulent FlowsFluid dynamics and aerodynamics studiesCombustion and flame dynamics

The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.

Thermal instability and convection of a thin fluid layer bounded by a stably stratified region

Whitehead, J. A., Chen, M. M.·1970·Journal of Fluid Mechanics
DOI 10.1017/s0022112070000319
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Abstract

Results of linear stability calculations and post-stability experimental observations are reported for horizontal fluid layers with upward heat flux bounded below by a stably stratified fluid. Stability calculations were done for several families of continuous and discontinuous temperature distributions, and it was found that as a rule the flow originating in the unstable layer penetrates into the stably stratified region, resulting in increased critical cell size and correspondingly decreased critical Rayleigh number. A notable exception to this occurs for an unstable layer with a linear temperature distribution adjacent to a stable layer of very high stable density gradient. In this case energy pumped from the unstable to the stable region is sufficient to raise the critical Rayleigh number above that of a solid boundary. It is also found that, for density distributions with a more gradual transition between the stable and the unstable regions, the effect of increased cell size upon the critical Rayleigh number is sometimes masked by effects of curvature in the density profile of the unstable region, which tends to increase the critical Rayleigh number. The inadequacy of the usual definition of Rayleigh number to characterize the stability of such complex systems is discussed. Experimentally, such a temperature distribution was produced by radiant energy from above as it was absorbed by the top few centimetres of the fluid. Within an uncertainty of ± 20%, it was found that the critical experimental Rayleigh number agreed with neutral stability calculations. The supercritical convective motion consisted of vertical jets of cool surface fluid which plunged downward into the interior of the fluid. The jets were not arranged in an orderly lattice but were in a constant state of change, each jet having a tendency to merge with a close neighbour. The net loss of jets due to merging was balanced by new jets spontaneously appearing. As Rayleigh number was increased, the mean number of jets and the intermittancy increased proportionally. Temperature scans taken with a movable probe showed that cool surface fluid plunging downward in the jets was confined to a fairly restricted region, the surrounding fluid being quite isothermal.

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Crossref · 10.1017/s0022112070000319

Cites

25 of 25 references verified0 citation errors · 0 not checkable

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  • Laboratory and numerical experiments suggest that the pattern will consist of sinking jets of cold fluid with upwelling elsewhere, and that it will be time dependent.

    “However the laboratory experiments of Whitehead & Chen (1970), Hooper and Tritton, as well as the numerical experiments of Thirlby (1970) and those described in Paper I, all suggest that the pattern will consist of sinking jets of cold fluid with upwelling occurring elsewhere, and that it will be time dependent.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Whitehead & Chen (1970)

  • All numerical and laboratory experiments on convecting fluids showed time-dependent motions.

    “Furthermore all experiments whether numerical or laboratory showed time-dependent motions.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Whitehead & Chen's (1970)

  • Laboratory experiments show that three-dimensional flow in uniformly heated fluid takes the form of sinking jets of cold fluid with upwelling elsewhere.

    “Whitehead & Chen's (1970) laboratory experiments show that the three-dimensional flow takes the form of sinking jets of cold fluid with upwelling taking place elsewhere.”

    From Speculations on the Thermal and Tectonic History of the Earth (2007) · cites this paper as Whitehead & Chen's (1970)

Citations

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Research works printed but not linked: 1

  1. Thompson, J. J. 1882 On a changing tesselated structure in certain liquids.Proc. Glasgow Phil. Soc. 13,464.

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Metadata

Authors
Whitehead, J. A., & Chen, M. M.
Affiliations
  • University of California, Los Angeles (US)
  • Yale University (US)
ORCID
Whitehead, J. A.
Venue
Journal of Fluid Mechanics
Publisher
Cambridge University Press (CUP)
Published
1970-02-18
Volume
40
Issue
3
Pages
549-576
ISSN
  • 0022-1120 (ISSN-L)
  • 1469-7645
DOI
10.1017/s0022112070000319
OpenAlex
W2091283816
Cited by
70
References
25
Citations by year
2026: 2 · 2022: 1 · 2021: 1 · 2018: 1 · 2015: 1 · 2014: 2 · 2013: 2
FWCI
2.30
Type
journal article
Language
en
Open access
closed
Licence
www.cambridge.org/core/terms (unspecified, 13188 d)
Locations
Journal of Fluid Mechanics (publishedVersion)
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 › Combustion and flame dynamics
Keywords
thermal instability, convection, stably stratified fluid, thin liquid layer, critical Rayleigh number, critical cell size, linear stability analysis, temperature distribution, density gradient, radiant heating, jet merging, intermittency

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