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Talk Abstract
Pattern formation in Rayleigh-Bénard convection at small Prandtl numbers and with rotation about a vertical axis

Institute for Mathematics and Its Applications
Guenter Ahlers, University of California Santa Barbara

This talk will discuss results from and future prospects for experimental studies of Rayleigh-Bénard convection with rotation about a vertical axis. At dimensionless rotation rates 0   $\leq$   $\Omega$   $\leq$ 20 and for Prandtl numbers $\sigma$ \simeq 1, measurements of Küppers-Lortz-unstable patterns have offered a unique opportunity to study spatio-temporal chaos immediately above a supercritical bifurcation. However, for $\Omega$   > 70 and $\sigma$ \simeq 1 patterns were found to be cellular near onset with local four-fold coordination. They differ from the theoretically expected Küppers-Lortz-unstable state. Stable as well as intermittent defect-free rotating square lattices exist in this parameter range.

Smaller Prandtl numbers ( 0.16   <   $\sigma$  <   0.7 ) can only be reached in mixtures of gases. These fluids are expected to offer rich future opportunities for the study of a line of tricritical bifurcations, of supercritical Hopf bifurcations, of a line of codimension-two points, and of a codimension-three point.

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