Rayleigh-Benard Convection

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Transition to Domain ChaosA debate between experiment and theory• Theory predicts scaling laws near threshold (Tu and Cross PRL, (1992))– How do quantities scale with the control parameter ɛ ?ɛ = constant × (∆T − ∆T c )∗ precession frequency should scale as ɛ 1.0• Experimenters find (Hu, Ecke and Ahlers, PRL, (1995))– Fits to much smaller power laws∗ precesssion frequency should scale as ɛ 0.6• Finite size effects may account for discrepancy(Cross, Louie, Meiron, PRE, (2001))
Domain ChaosSupercomputer solutions of fluid equations with rotation (Coriolis force)Start with Periodic system
Page 2: What is pattern formation?• Many
Page 6 and 7: Examples from the laboratory• Bel
Page 8 and 9: Examples from the laboratory• Bel
Page 11 and 12: Rayleigh-Bénard Convectionphotos c
Page 13: Stability DiagramFor Rayleigh-Béna
Page 17 and 18: Domain chaosParameters are exactly
Page 19 and 20: Centrifugal Force cannot be neglect
Page 21 and 22: Other work-Lyapunov Exponents• Ch
Page 23 and 24: Visualization of temperature fieldc
Page 25 and 26: Visualization of temperature pertur
Page 27 and 28: Future work• Short Term- Incorpor

Rayleigh-Benard Convection

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