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Patterns in Rotating Rayleigh-B énard Convection at High Rotation Rates

Patterns in Rotating Rayleigh-B énard Convection at High Rotation Rates. Presented by: P. L. Mutyaba pmutyaba@clunet.edu P. L. Mutyaba, Terri Kimmel, Janet D. Scheel California Lutheran University. Rotation, Ω. Rayleigh-B énard Convection (RBC). R a. Side View.

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Patterns in Rotating Rayleigh-B énard Convection at High Rotation Rates

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

  2. Rotation,Ω Rayleigh-Bénard Convection (RBC) Ra Side View http://www.chemistrydaily.com/chemistry/upload/1/12/Convection_cells.png

  3. Square Patterns in RBC • Bulk • Square • Periphery • Traveling wave Overhead View

  4. Previous Research • Experiments • Rotation rates • 170 • Cylindrical cells • Aspect ratio 5 and 3 (radius to depth ratio) Bajaj et al.(1998)

  5. 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 • Aspect Ratio is 5, Ω = 274, ε=0.02 • Oscillating Rolls • KL Instability • 90 °

  9. Periodic Cell • Non-random initial condition • Super-imposed rolls, fade in and out • Not a transient state • Traveling wave is not necessary.

  10. Results Aspect Ratio = 5, Ω=170, ε=0.09 Coriolis and centrifugal forces

  11. Results Aspect Ratio = 5, Ω=170 , ε =0.09 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) Coriolis and centrifugal forces Bajaj et al.(1998) Coriolis force

  13. 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 ) Sánchez-Álvarez et al.(2005) Coriolis and centrifugal forces Coriolis force

  14. 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. Conclusion

  15. 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 Future Work

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

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