1. Patterns in Rotating Rayleigh-Bénard Convection at High Rotation Rates
Presented by: P. L. Mutyaba
P. L. Mutyaba, Terri Kimmel, Janet D. Scheel
California Lutheran University

2. Rayleigh-Bénard Convection (RBC)
Rotation,Ω Ra
Side View
Ra –Temperature difference

3. Square Patterns in RBC Bulk Periphery Square Traveling wave
Horizontal slice at mid plane.
Overhead View

4. Previous Research Experiments Rotation rates 170 Cylindrical cells
Aspect ratio 5 and 3
(radius to depth ratio)
This was taken at an epsilon value of 0.09
Bajaj et al.(1998)

5. Sánchez-Álvarez et al.(2005)
Previous Research
Numerical Simulations
Aspect Ratio 5 and 3
Ω =274
Aspect Ratio 3
Ω =180
Observations
Traveling wave affects bulk
Sánchez-Álvarez et al.(2005)

6. Current Research Goals Accurately simulate experiments
Investigate interaction between the traveling wave and bulk
Study effect of centrifugal forces on square pattern formation

7. Methods Boussinesq Equations Code written by Paul Fischer (Argonne)
Experimentally realistic boundary conditions
No slip for the velocity

8. Periodic Cell Random initial conditions Parameters KL Instability
Aspect Ratio is 5,
Ω = 274, ε=0.02
Oscillating Rolls
KL Instability
90 °
The KL state does come in after the oscillating squares

9. Periodic Cell Non-random initial condition
Super-imposed rolls, fade in and out
Not a transient state
Traveling wave is not necessary.
Blank out the time and include the angles
No conclusive evidence of stabilization of the bulk by tw

10. Results Aspect Ratio = 5, Ω=170, ε=0.09
Convert to epsilon –all slides, all rayleigh numbers
Coriolis and centrifugal forces

11. Results
Aspect Ratio = 5, Ω=170 , ε =0.09
Include
Coriolis force only

12. Discussion
The inclusion of the centrifugal and Coriolis forces provides better agreement with experiment. (Aspect Ratio = 5, Ω=170, ε=0.09)
Include parameters( rotation rate and Ra)
Coriolis and centrifugal forces
Bajaj et al.(1998)
Coriolis force

13. Sánchez-Álvarez et al.(2005)
Discussion
The inclusion of the Coriolis force only provides better agreement with other numerical simulations. (Aspect Ratio = 5,Ω=274,ε =0.004, ε=0.02 )
Include rotation rate and Ra and also remember to talk about the epsilon and how it gives a measure of how above threshold we are runnning the simulations at .
Sánchez-Álvarez et al.(2005)
Coriolis and centrifugal forces
Coriolis force

14. Conclusion
The oscillating rolls may be Küppers-Lortz Instability with a switching angle of 90 °.
The centrifugal force should be included in order to numerically model the RBC experiments.

15. Future Work
The effects of the fictitious forces on the growth rates of the modes are necessary to understand pattern formation.
The cause of the square patterns
The oscillation of the square bulk

16. Acknowledgements Dr. Janet Scheel Terri Kimmel Sam Walton
Katelyn White
Dr. Michael Cross
The Swenson Family