#### Transcript Patterns in Rotating Rayleigh-Bénard Convection at High Rotation

Patterns in Rotating Rayleigh-Bénard Convection at High Rotation Rates Presented by: P. L. Mutyaba [email protected] P. L. Mutyaba, Terri Kimmel, Janet D. Scheel California Lutheran University Rayleigh-Bénard Convection (RBC) Rotation, Ω Ra Side View http://www.chemistrydaily.com/chemistry/upload/1/12/Convection_cells.png Square Patterns in RBC Bulk Square Periphery Traveling wave Overhead View Previous Research Experiments Rotation rates 170 Cylindrical cells Aspect ratio 5 and 3 (radius to depth ratio) Bajaj et al.(1998) Previous Research Numerical Simulations Aspect Ω =274 Aspect Ratio 5 and 3 Ratio 3 Ω =180 Observations Traveling wave affects bulk Sánchez-Álvarez et al.(2005) Current Research Goals Accurately simulate experiments Investigate interaction between the traveling wave and bulk Study effect of centrifugal forces on square pattern formation Methods Boussinesq Equations ( t u )u - p 2u - gzˆ 2zˆ u 2 r, ( t u ) 2 , and u 0 Code written by Paul Fischer (Argonne) Experimentally realistic boundary conditions No slip for the velocity Periodic Cell Random initial conditions Parameters Aspect Ratio is 5, Ω = 274, ε=0.02 Oscillating Rolls KL Instability 90 ° Periodic Cell Non-random initial condition Super-imposed rolls, fade in and out Not a transient state Traveling wave not necessary. is Results Aspect Ratio = 5, Ω=170, ε=0.09 Coriolis and centrifugal forces Results Aspect Ratio = 5, Ω=170 , ε =0.09 Coriolis force only Discussion The inclusion of the centrifugal and Coriolis forces provides better agreement with experiment. (Aspect Ratio = 5, Ω=170, ε=0.09) Bajaj et al.(1998) Coriolis and centrifugal forces Coriolis force 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 Conclusion The oscillating rolls may be KüppersLortz Instability with a switching angle of 90 °. The centrifugal force should be included in order to numerically model the RBC experiments. 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 Acknowledgements Dr. Janet Scheel Terri Kimmel Sam Walton Katelyn White Dr. Michael Cross The Swenson Family