THE CENTER FOR NONLINEAR STUDIES

PROGRAM
Tuesday
May 23, 2000

1:00pm-2:00pm

Lecture I: Turbulent Heat Transport in Fluids Heated 

from Below

One of the central issues in turbulent convection of a fluid heated from below has been the global heat transport, as expressed by the Nusselt number A number of theoretical models have predicted powerlaw relations between N and the Rayleigh number R. New high precision measurements will be discussed which show that simple powerlaws are not adequate for this purpose. On the other hand, a model recently proposed by Grossmann and Lohse (GL) and based on the decomposition of the kinetic and the thermal dissipation into boundary-layer and bulk contributions gives an excellent fit to the R-dependence. Unfortunately, the Prandtl-number dependence, which is given as well by the GL model, does not agree with experiment.

 
Tuesday
May 23, 2000


3:00pm-4:00pm

Lecture II: Pattern Formation near Onset of Rayleigh-Benard Convection: Some Simple Unexplained Results.

Although much is known about pattern formation in nonlinear dissipative systems, there are several seemingly simple experimentally observed phenomena which either remain unexplained, or on which experiment and theory disagree. This is so even near the threshold of pattern formation where weakly nonlinear theories should be applicable. This talk will discuss 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 (Rayleigh-Benard convection). Issues to be addressed will include wavenumber selection near onset, the effect of a Coriolis force on pattern formation, and convection with rotation at small Prandtl numbers.
Wednesday
May 24, 2000

10:00am-11:00am

Lecture III: Critical Phenomena near Bifurcations in Systems far from Equilibrium

In spatially-extended nonlinear dissipative systems far from equilibrium, bifurcations are usually discussed in terms of deterministic equations for the macroscopic variables which neglect the "microscopic" degrees of freedom. An example is the use of the NavierStokes equation for Rayleigh-Benard convection (RBC). There is then a sharp bifurcation point R=Rc at which an exchange of stability occurs between the spatially-uniform state and the state with spatial variation. 

If the system is subjected to external noise, then even below the bifurcation there are fluctuations of the macroscopic variables away from the uniform state. The relevant fields then each have zero mean but a positive (albeit small) mean square. This talk will review the experimental measurements of the properties of these fluctuations. In the case of RBC, the exponents of the powerlaws which describe these properties have their classical (mean-field) values. However, for electroconvection in a nematic liquid crystal (which is more susceptible to noise) there are deviations from the classical behavior when the system comes within a few percent of the bifurcation point. As near equilibrium critical points, the exponent values then differ from the classical ones.

 

Refreshments Will Be Served Following Each Lecture