Rayleigh-Benard Convection

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ResultsScaling of defect velocities agrees well with theorywhich predicts V glide scales as ɛ 0.75F CorF Cor, periodicslope=0.71v glide10 0 ε10 −1slope=0.7510 −3 10 −2 10 −1Scheel and Cross, PRE, 72
Other work-Lyapunov Exponents• Chaos exhibits the “Butterfly Effect”—sensitivity to Initial Conditions• “Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado inTexas?” —Lorenz, 1972• Lyapunov Exponent λ is a measure of this sensitivity to initialconditions: δu(t) = δu(0)e λt• Positive Lyapunov Exponent → exponential divergence of nearbytrajectories δu(0) → system is chaotic→
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 and 14: Stability DiagramFor Rayleigh-Béna
Page 15 and 16: Domain ChaosSupercomputer solutions
Page 17 and 18: Domain chaosParameters are exactly
Page 19: Centrifugal Force cannot be neglect
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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