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On the Boussinesq Approximation for a Compressible Fluid.
Abstract
The full, non4inear equations governing thermal convection in a compressible fluid have been re-examined in order to determine the conditions under which the Boussinesq approximation is applicable These conditions are (a) the vertical dimension of the fluid is much less than any scale height, and (b) the motion-induced fluctuations in density and pressure do not exceed, in order of magnitude, the total static variations of these quantities. Under these conditions the equations are formally equivalent to those for an incompressible system when the temperature gradient is replaced by its excess over the adiabatic and Cp replaces C .
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Citations
Cited by
Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation
Vallis, G. K. (2017) · doi:10.1017/9781107588417 · Cited by 1,891
The validity of the boussinesq approximation for liquids and gases
Gray, D. D., & Giorgini, A. (1976) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(76)90168-x · Cited by 1,120
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
New perspectives in turbulent Rayleigh-Bénard convection
Chillà, F., & Schumacher, J. (2012) · The European Physical Journal E · doi:10.1140/epje/i2012-12058-1 · Cited by 746
Double-Diffusive Convection at Low Prandtl Number
Garaud, P. (2018) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-122316-045234 · Cited by 198
Metadata
- Authors
- Spiegel, E. A., & Veronis, G.
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 1960-03
- Volume
- 131
- Pages
- 442
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W2049923710
- Cited by
- 973
- References
- 0
- FWCI
- 3.51
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: On the Boussinesq Approximation for a Compressible Fluid. https://app.cochat.ai/papers/10.1086/146849
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- Spiegel, E. A., & Veronis, G. (1960). On the Boussinesq Approximation for a Compressible Fluid. The Astrophysical Journal. https://doi.org/10.1086/146849
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