Pattern formation near onset of Rayleigh-Bénard convection: Some simple unexplained results

Guenter Ahlers
Center for Nonlinear Science and Department of Physics
University of California, Santa Barbara

Our goals as experimentalists in the field of pattern formation fall into three categories:

  1. Test already existing theoretical predictions;
  2. Find qualitatively new phenomena which are simple enough to be understood in the not too distant future;
  3. Design simple "idealized" experiments illustrating important general phenomena.

This talk will illustrate how these goals are pursued, by discussing a number of studies of pattern formation under carefully controlled conditions near the onset of convection in a shallow horizontal layer of a fluid heated from below.

The first part of the talk will be devoted to experimental results for convection-roll selected in a cylindrical sample which had an interior section of uniform spacing. For Rayleigh numbers above the critical value in the interior, straight or slightly curved rolls were selected. It is observed that in some regimes, the pattern repeatedly formed defects. The defects moved in the direction of the perturbation associated with the instability responsible for their formation.

In the second half of the talk, the effect of a Coriolis force due to rotation of a sample with rigid sidewalls (no ramp) about a vertical axis will be considered. At small dimensionless rotation rates appropriate Prandtl numbers domain chaos was found immediately above a supercritical bifurcation. The dependence of the time and length scales of the chaotic state on the Rayleigh number differed from the theoretically expected dependence. For other values, the patterns differed from the theoretically expected chaotic state. Instead, rotating square patterns were found. Finally, some opportunities for future work will be mentioned.