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Numerical study of pattern forming processes in models of rotating Rayleigh-Bénard convection

Citation

Louie, Michael (2001) Numerical study of pattern forming processes in models of rotating Rayleigh-Bénard convection. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:10132010-082113565

Abstract

In this thesis we numerically study two unique pattern forming processes observed in Rayleigh-Bénard convection. Using variants of the Swift-Hohenberg equation, we study the Küppers-Lortz instability and a spiral chaos state in a large cylindrical cell. For the Küppers-Lortz instability, we show that the theoretical scaling of the correlation length and domain switching frequency hold in the case of our model equations. We find, however, that it is necessary to account for finite size effects by scaling the correlation length appropriately. We find then that the correlation length scales linearly with the size of the cell when the cell is small and/or when the control parameter is small. Scaling of the domain switching frequency for finite size effects is not necessary as domain switching appears to be enhanced by sidewall processes. Our results provide strong evidence that finite size effects are responsible for the observed discrepancies between theoretical and experimental scalings. We also study the effect of rotation on the spiral state which occurs in a Swift-Hohenberg equation through a coupling with mean flow effects. We find that rotation and mean flow are competing processes. Mean flow shifts the pattern wave number so that the usual Küppers-Lortz instability is only observed at higher rotation rates. A parameter search is performed and a consistent trend of patterns is observed as the rotation rate is increased.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Cross, Michael Clifford (advisor)
  • Meiron, Daniel I. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 June 2000
Record Number:CaltechTHESIS:10132010-082113565
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:10132010-082113565
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6141
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:13 Oct 2010 15:39
Last Modified:26 Dec 2012 04:31

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