Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T23:34:46.859Z Has data issue: false hasContentIssue false

Standing and travelling oscillatory blob convection

Published online by Cambridge University Press:  26 April 2006

R. M. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90024, USA and Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90024, USA and Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany

Abstract

Results of numerical computations are presented of time-dependent three-dimensional convection flows in a horizontal layer heated from below which evolve from the oscillatory blob instability of steady two-dimensional rolls. It is shown that the heat transport is typically increased in the transition to blob convection. Oscillatory blob convection exists in the forms of standing or travelling blob convection. The latter type of solution represents the stable form bifurcating supercritically at the Rayleigh number RII for the onset of the oscillatory blob instability. In contrast to standing blob convection travelling blob convection exhibits a mean flow.

Type
Research Article
Copyright
© 1995 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

Bolton, E. W., Busse, F. H. & Clever, R. M. 1986 Oscillatory instabilities of convection rolls at intermediate Prandtl numbers. J. Fluid Mech. 164, 469485.Google Scholar
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46, 140150.Google Scholar
Busse, F. H. 1981 Transition to turbulence in Rayleigh-Bénard convection. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub). Springer.
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319335.Google Scholar
Busse, F. H. & Clever, R. M. 1990 Transitions to more complex patterns in thermal convection. In New Trends in Nonlinear Dynamics and Pattern Forming Phenomena: The Geometry of Nonequilibrium (ed. P. Coullet & P. Huerre), pp. 3745. NATO ASI Series, Plenum.
Busse, F. H. & Hood, L. L. 1982 Differential rotation driven by convection in a rotating annulus. Geophys. Astrophys. Fluid Dyn. 21, 5974.Google Scholar
Busse, F. H., Kropp, M. & Zaks, M. 1992 Spatio-temporal structures in phase-turbulent convection. Physica D 61, 94105.Google Scholar
Chen, M. M. & Whitehead, J. A. 1968 Evolution of two-dimensional periodic Rayleigh convection cells of arbitrary wavenumbers. J. Fluid Mech. 31, 115.Google Scholar
Clever, R. M. & Busse, F. H. 1987 Nonlinear oscillatory convection. J. Fluid Mech. 176, 403417.Google Scholar
Clever, R. M. & Busse, F. H. 1988 Three-dimensional knot convection in a layer heated from below. J. Fluid Mech. 198, 345363.Google Scholar
Clever, R. M. & Busse, F. H. 1989 Nonlinear oscillatory convection in the presence of a vertical magnetic field. J. Fluid Mech. 201, 507523.Google Scholar
Clever, R. M. & Busse, F. H. 1990 Convection at very low Prandtl numbers. Phys. Fluids A 2, 334339.Google Scholar
Clever, R. M. & Busse, F. H. 1993 Convection in a fluid layer with asymmetric boundary conditions. Phys. Fluids A 5, 99107.Google Scholar
Clever, R. M. & Busse, F. H. 1994 Steady and oscillatory bimodal convection. J. Fluid Mech. 271, 103118.Google Scholar
Curry, T. B., Herring, J. R., Loncaric, J. & Orszag, S. A. 1984 Order and disorder in two- and three-dimensional Bénard convection. J. Fluid Mech. 147, 138.Google Scholar
Frick, H., Busse, F. H. & Clever, R. M. 1983 Steady three-dimensional convection at high Prandtl number. J. Fluid Mech. 127, 141153.Google Scholar
Gollub, J. P., Mccarriar, A. R. & Steinman, I. F. 1982 Convective pattern evolution and secondary instabilities. J. Fluid Mech. 125, 259281.Google Scholar
Golubitsky, M. & Stewart, I. 1989 Hopf bifurcation in the presence of symmetry. Arch. Rat. Mech. Anal. 87, 107165.Google Scholar
Howard, L. N. 1966 Convection at high Rayleigh number. In Proc. 11th Intl Congr. Appl. Mech., Munich 1964 (ed. H. Görtler), pp. 11091115. Springer.
Howard, L. N. & Krishnamurti, R. 1986 Large-scale flow in turbulent convection: a mathematical model. J. Fluid Mech. 170, 385410.Google Scholar
Krishnamurti, R. & Howard, L. N. 1981 Large-scale flow generation in turbulent convection. Proc. Natl Acad. Sci. USA 78, 19811985.Google Scholar
Lennie, T. B., Mckenzie, D. P., Moore, D. R. & Weiss, N. O. 1988 The breakdown of steady convection. J. Fluid Mech. 188, 4785.Google Scholar
Or, A. C. & Busse, F. H. 1987 Convection in a rotating cylindrical annulus. Part 2. Transitions to asymmetric and vacillating flows. J. Fluid Mech. 174, 313326.Google Scholar
Prat, J., Massaguer, J. M. & Mercader, I. 1995 Large-scale flows and resonances in 2-D thermal convection. Phys. Fluids 7, 121134.Google Scholar
Schecter, S. 1976 Bifurcations with symmetry. In The Hopf Bifurcation and its Applications (ed. J. E. Marsden & M. McCracken), pp. 224249. Springer.
Schmitt, B. J. & Wahl, W. VON 1992 Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations. In The Navier- Stokes Equations II - Theory and Numerical Methods (ed. J. G. Heywood, K. Masuda, R. Rautmann, S. A. Solonnikov). Lecture Notes in Mathematics, vol. 1530, pp. 291305. Springer.
Solomon, T. H. & Gollub, J. P. 1990 Sheared boundary layers in turbulent Rayleig-Bénard Convection. Phys. Rev. Lett. 64, 23822385.Google Scholar
Zippelius, A. & Siggia, E. D. 1983 Stability of finite amplitude convection. Phys. Fluids 26, 29052915.Google Scholar
Zocchi, G., Moses, E. & Libchaber, A. 1990 Coherent structures in turbulent convection, an experimental study. Physica A 166, 387407.Google Scholar