Summary: Wave-number Selection by Target Patterns and Side Walls in Rayleigh-B´enard
John R. Royer, Patrick O'Neill, Nathan Becker, and Guenter Ahlers
Department of Physics and iQUEST,
University of California, Santa Barbara, CA 93106
(Dated: April 27, 2004)
We present experimental results for patterns of Rayleigh-B´enard convection in a cylindrical con-
tainer with static side-wall forcing. The fluid used was methanol, with a Prandlt number = 7.17,
and the aspect ratio was R/d 19 (R is the radius and d the thickness of the fluid layer).
In the presence of a small heat input along the side wall, a sudden jump of the temperature differ-
ence T from below to slightly above a critical value Tc produced a stable pattern of concentric
rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell. A quasi-static
increase of T/Tc - 1 beyond 1,c 0.8 caused the umbilicus of the pattern to move off
center. As observed by others, a further quasi-static increase of up to = 15.6 caused a sequence
of transitions at i,b, i = 1, ..., 8, each associated with the loss of one convection roll at the umbilicus.
Each loss of a roll was preceded by the displacement of the umbilicus away from the center of the
cell. After each transition the umbilicus moved back toward but never quite reached the center.
With decreasing new rolls formed at the umbilicus when was reduced below i,a < i,b. When
decreasing , large umbilicus displacements did not occur.
In addition to quantitative measurements of the umbilicus displacement, we determined and