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Three-dimensional knot convection in a layer heated from below

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

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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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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