Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-28T17:08:36.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical solutions of single-mode convection equations

Published online by Cambridge University Press:  11 April 2006

Juri Toomre ,
D. O. Gough  and
E. A. Spiegel
Juri Toomre
Affiliation:
Joint Institute for Laboratory Astrophysics and Department of Astro-Geophysics, University of Colorado, Boulder
D. O. Gough
Affiliation:
Institute of Astronomy and Department of Applied Mathematics and Theoretical Physics, University of Cambridge
E. A. Spiegel
Affiliation:
Astronomy Department, Columbia University, New York 10027
Get access Rights & Permissions [Opens in a new window]

Abstract

sfjsdjfsdfsdfjsdjfsf

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 1 , 20 January 1977 , pp. 1 - 31
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, N. H., Moore, D. W. & Spiegel, E. A. 1971 Aperiodic behavior of a non-linear oscillator. Quart. J. Mech. Appl. Math. 24, 391–422.Google Scholar
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67–80.Google Scholar
Chan, S. K. 1971 Infinite Prandtl number turbulent convection. Studies in Appl. Math. 50, 13–49.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141–159.Google Scholar
Deardorff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675–704.Google Scholar
Fitzjarrald, D. E. 1975 An experimental study of turbulent convection in air. J. Fluid Mech. 73, 693–719.Google Scholar
Garon, A. M. & Goldstein, R. J. 1973 Velocity and heat transfer measurements in thermal convection. Phys. Fluids, 16, 1818–1825.Google Scholar
Globe, S. & Dropkin, D. 1959 Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. J. Heat Transfer, 81, 24–28.Google Scholar
Goldstein, R. J. & Chu, T. Y. 1971 Thermal convection in a horizontal layer of air. Prog. Heat Mass Transfer, 2, 55–75.Google Scholar
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975a Modal equations for cellular convection. J. Fluid Mech. 68, 695–719.Google Scholar
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975b Highly stretched meshes as functional of solutions. Proc. 4th Int. Conf. Numer. Meth. Fluid Mech. (ed. R. D. Richtmyer), pp. 191–196. Lecture Notes in Physics, vol. 35. Springer.
Henrici, P. 1962 Discrete Variable Methods in Ordinary Differential Equations. Wiley.
Herring, J. R. 1963 Investigations of problems in thermal convection. J. Atmos. Sci. 20, 325–338.Google Scholar
Herring, J. R. 1964 Investigation of problems in thermal convection: rigid boundaries. J. Atmos. Sci. 21, 277–290.Google Scholar
Howard, L. N. 1966 Convection at high Rayleigh number. Proc. 11th Int. Cong. Appl. Mech. (ed. H. Görtler), pp. 1109–1115. Springer.
Jones, C. A., Moore, D. R. & Weiss, N. O. 1975 Axisymmetric convection in a cylinder. J. Fluid Mech. 73, 353–388.Google Scholar
Kraichnan, R. J. 1962 Mixing-length analysis of turbulent thermal convection at arbitrary Prandtl numbers. Phys. Fluids, 5, 1374–1389.Google Scholar
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Ledoux, P., Schwarzschild, M. & Spiegel, E. A. 1961 On the spectrum of turbulent convection. Astrophys. J. 133, 184–197.Google Scholar
Lipps, F. B. & Somerville, R. C. J. 1971 Dynamics of variable wavelength in finiteamplitude Bénard convection. Phys. Fluids, 14, 759–765.Google Scholar
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. Roy. Soc. A225, 185–195.Google Scholar
Malkus, W. V. R. 1954b The heat transport and spectrum of thermal turbulence. Proc. Roy. Soc. A225, 196–212.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Murphy, J. O. 1971a Nonlinear thermal convection with free boundaries. Aust. J. Phys. 24, 587–592.Google Scholar
Murphy, J. O. 1971b Non-linear convection with hexagonal planform. Proc. Astron. Soc. Austr. 2, 53–54.Google Scholar
Priestley, C. H. B. 1954 Turbulent Transfer in the Lower Atmosphere. University of Chicago Press.
Roberts, P. H. 1966 On non-linear Bénard convection. Non-Equilibrium Thermodynamics, Variational Techniques, and Stability (ed. R. Donnelly, R. Hermann & I. Prigogine), pp. 125–162. University of Chicago Press.
Rossby, H. T. 1966 An experimental study of Bénard convection with and without rotation. Ph.D. thesis, Massachusetts Institute of Technology.
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Schmidt, R. J. & Saunders, O. A. 1938 On the motion of a fluid heated from below. Proc. Roy. Soc. A165, 216–228.Google Scholar
Silveston, P. L. 1958 Wärmedurchgang in Waagerechten Flüssigkeitsschichten. Forsch. Ing. Wes. 24, 59–69.Google Scholar
Somerscales, E. F. C. & Dropkin, D. 1966 Experimental investigation of the temperature distribution in a horizontal layer of fluid heated from below. Int. J. Heat Mass Transfer, 9, 1189–1204.Google Scholar
Somerscales, E. F. C. & Gazda, I. W. 1969 Thermal convection in high Prandtl number liquids at high Rayleigh numbers. Int. J. Heat Mass Transfer, 12, 1491–1511.Google Scholar
Spiegel, E. A. 1962 Thermal turbulence at very small Prandtl number. J. Geophys. Res. 67, 3063–3070.Google Scholar
Spiegel, E. A. 1971 Convection in stars. I. Basic Boussinesq convection. Ann. Rev. Astron. Astrophys. 9, 323–352.Google Scholar
Stewartson, K. 1966 Asymptotic theory in limit R. Non-Equilibrium Thermodynamics, Variational Techniques, and Stability (ed. R. Donnelly, R. Hermann & I. Prigogine), pp. 158–162. University of Chicago Press.
Thomas, D. B. & Townsend, A. A. 1957 Turbulent convection over a heated horizontal surface. J. Fluid Mech. 2, 473–492.Google Scholar
Threlfall, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 17–28.Google Scholar
Veltishchev, N. F. & Želnin, A. A. 1975 Numerical simulation of cellular convection in air. J. Fluid Mech. 68, 353–368.Google Scholar
Veronis, G. 1966 Large-amplitude Bénard convection. J. Fluid Mech. 26, 49–68.Google Scholar
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux. J. Fluid Mech. 54, 351–367.Google Scholar