Journal of Fluid Mechanics

Three-dimensional knot convection in a layer heated from below

R. M.  Clever a1 and F. H.  Busse a2
a1 Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA 90024, USA
a2 Institute of Physics, University of Bayreuth, Postfach 10 1251, 8580 Bayreuth, FRG

Article author query
clever rm   [Google Scholar] 
busse fh   [Google Scholar] 


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.

(Published Online April 21 2006)
(Received December 30 1987)