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Three-dimensional knot convection in a layer heated from below

  • R. M. Clever (a1) and F. H. Busse (a2)
Abstract

Steady three-dimensional convection flows induced by the knot instability of two-dimensional convection rolls are studied numerically for various Prandtl numbers. The Galerkin method is used to obtain the three-dimensional solutions of the basic equations in the case of rigid, infinitely conducting boundaries. These solutions exhibit the typical knot-like structure superimposed onto the basic rolls. The Nusselt number and kinetic energy of motion do not differ much for two- and three-dimensional solutions and the toroidal part of the kinetic energy associated with vertical vorticity always remains a small fraction of the total in the case of the knot solution. The analysis of the steady solutions is complemented by a stability analysis with respect to disturbances that fit the same horizontal periodicity interval as the knot solution. All instabilities correspond to Hopf bifurcations. Some example of finite-amplitude oscillatory knot convection are presented.

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Bolton, E. W., Busse, F. H. & Clever, R. M., 1986 Oscillatory instabilities of convection rolls at intermediate Prandtl numbers. J. Fluid Mech. 164, 469485.
Busse, F. H.: 1967 On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46, 140150.
Busse, F. H.: 1978 Nonlinear properties of convection. Rep. Prog. Phys. 41, 19291967.
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). Topics in Applied Physics, vol. 45, pp. 97137. Springer.
Busse, F. H. & Clever, R. M., 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319335.
Busse, F. H. & Frick, H., 1985 Square pattern convection in fluids with strongly temperature dependent viscosity. J. Fluid Mech. 150, 451465.
Busse, F. H. & Whitehead, J. A., 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 6779.
Chandrasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Clever, R. M. & Busse, F. H., 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625645.
Clever, R. M. & Busse, F. H., 1987 Nonlinear oscillatory convection. J. Fluid Mech. 176, 403417.
Curry, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A., 1984 Order and disorder in two- and three-dimensional Bénard convection. J. Fluid Mech. 147, 138.
Frick, H., Busse, F. H. & Clever, R. M., 1983 Steady three-dimensional convection at high Prandtl number. J. Fluid Mech. 127, 141153.
Grötzbach, G.: 1982 Direct numerical simulation of laminar and turbulent Bénard convection. J. Fluid Mech. 119, 2753.
Lipps, F. B.: 1976 Numerical simulation of three-dimensional Bénard convection in air. J. Fluid Mech. 75, 113148.
McLaughlin, J. B. & Orszag, S. A., 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123142.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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