1. Physics 313: Lecture 2 Wednesday, 8/27/08

2. Comments to the Class
Get in habit of reading Announcements link of 313 web page before each class.
Lecture files change within a few days after lecture.
Extra meeting this week to discuss homework, related background material?
Topics:
Finish canonical example of a pattern-forming nonequilibrium system, R and Rc.
Discussion of examples: what are the interesting scientific questions?
When are natural systems high-dimensional and so need new approaches?

3. Rayleigh-Benard Convection: Canonical Pattern-Forming System

4. Cloud Street: Clouds in Convecting Layer

5. How Patterns Observed? Shadowgraphy

6. Buoyancy Force Versus Dissipation From Viscosity and Thermal Conduction

7. Dimensionless “Driving” or Bifurcation Parameter: the Rayleigh Number R
Nonequilibrium systems characterized by one or more dimensionless parameters, of which one is often a ratio of “driving” to “dissipation”.
Starting from thermal equilibrium, nothing happens until driving parameter exceeds critical value Rc ~ 1708.
Rayleigh number, Prandtl number, Reynolds number famous parameters in fluid dynamics.
Worked example of where dimensionless parameters come from.

8. Example Using the Rayleigh Number

9. Worked Example: Where Dimensionless Parameters Like R Come from

10. Convection Patterns Unique patterns? What sets the length scale?
Unique patterns?
What sets the length scale?
Unique wavelength?
Rotation speed?

11. Chaotic Convection Patterns

12. Discussion: Are These Spatiotemporal Chaotic Patterns Different?

13. Effect of Pattern Formation on Transport

14. Almost Periodicity Common Feature:Defects

15. Crispation Patterns (Faraday Waves)