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Instabilities of longitudinal convection rolls in an inclined layer

Published online by Cambridge University Press:  12 April 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Structures Department, University of California, Los Angeles
F. H. Busse
Affiliation:
Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

The stability of longitudinal rolls in an inclined convection layer is investigated for various angles of inclination. Three types of instability are responsible for the transition from longitudinal rolls to three-dimensional forms of convection in different regimes of the parameter space. The role of the wavy instability is emphasized since it does not correspond to a transition in the case of a horizontal layer. The analysis emphasizes the cases of air and water as convective media. Comparison of the theoretical results with experimental data indicates that the stability analysis based on infinitesimal disturbances correctly describes the observed instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 1 , 9 June 1977 , pp. 107 - 127
Copyright
© 1977 Cambridge University Press

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References

Bénard, H. & Avsec, D. 1938 Travaux récents sur les tourbillons cellulaires et les tourbillons en bandes. Applications a l'astrophysique et la météorologie. J. Phys. Radium 9, 486–500.Google Scholar
Busse, F. H. 1967a On the stability of two-dimensional convection in a layer heated from below. J. Math. & Phys. 46, 140–150.Google Scholar
Busse, F. H. 1967b The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649.Google Scholar
Busse, F. H. 1971 In Instability of Continuous Systems (ed. H. Leipholz), pp. 41–47. Springer.
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid. J. Fluid Mech. 52, 97–112.Google Scholar
Busse, F. H. & Clever, R. M. 1977 The knot instability of convection rolls in fluids of moderate Prandtl numbers. (In preparation.)
Busse, F. H. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid. J. Fluid Mech. 47, 305–320.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Clever, R. M. 1973 Finite amplitude longitudinal convection rolls in an inclined layer. J. Heat Transfer 95, 407–408.Google Scholar
Clever, R. M. 1977 The stability and heat transfer of two-dimensional convection in an internally heated fluid layer. Z. angew. Math. Phys. (in press).
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Coles, D. 1965 Transition, in circular Couette flow. J. Fluid Mech. 21, 385–425.Google Scholar
Davey, A., DiPrima, R. C. & Stuart, J. T. 1968 On the stability of Taylor vortices. J. Fluid Mech. 31, 17–52.Google Scholar
Denny, V. E. & Clever, R. M. 1974 Comparisons of Galerkin and finite difference methods for solving highly nonlinear thermally driven flows. J. Comp. Phys. 16, 271–284.Google Scholar
Gershuni, G. Z. & Zhukovitskii, E. M. 1969 Stability of plane parallel convective motion with respect to spatial perturbations. Prikl. Math. Mech. 33, 830–835.Google Scholar
Hart, J. E. 1971a The stability of flow in a differentially heated inclined box. J. Fluid Mech. 47, 547–576.Google Scholar
Hart, J. E. 1971b Transition to a wavy vortex regime in convective flow between inclined plates. J. Fluid Mech. 48, 265–271.Google Scholar
Hart, J. E. 1973 A note on the structure of thermal convection in a slightly slanted slot. Int. J. Heat Mass Transfer 16, 747–753.Google Scholar
Korpela, S. A., Gözüm, D. & Chandakant, B. B. 1973 On the stability of the conduction regime of natural convection in a vertical slot. Int. J. Heat Mass Transfer 16, 1683–1690.Google Scholar
Krishnamurti, R. 1970a On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Krishnamurti, R. 1974 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Lipps, F. B. 1971 Two-dimensional numerical experiments in thermal convection with vertical shear. J. Atmos. Sci. 28, 3–19.Google Scholar
Richter, F. & Parsons, B. 1975 On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80, 2529–2541.Google Scholar
Richter, F. & Whitehead, J. A. 1974 Rayleigh — Bénard convection at large Prandtl numbers with shear. Bull. Am. Phys. Soc. 19, 1159.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. H. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Snyder, A. A. 1970 Waveforms in rotating Couette flow. Int. J. Non-Linear Mech. 5, 659–685.Google Scholar
Sparrow, E. M. & Husar, R. B. 1969 Longitudinal vortices in natural convection flow on inclined plates. J. Fluid Mech. 37, 251–255.Google Scholar
Squire, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. Roy. Soc. 142, 621–628.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661–672.Google Scholar