Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media

Peter Vadasz, Shmuel Olek

Research output: Contribution to journalArticle

73 Scopus citations

Abstract

Low Prandtl number convection in porous media is relevant to modern applications of transport phenomena in porous media such as the process of solidification of binary alloys. The transition from steady convection to chaos is analysed by using Adomian's decomposition method to obtain an analytical solution in terms of infinite power series. The practical need to evaluate the solution and obtain numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task, transform the analytical results into a computational solution evaluated up to a finite accuracy. The solution shows a transition from steady convection to chaos via a Hopf bifurcation producing a 'solitary limit cycle' which may be associated with an homoclinic explosion. This occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. Periodic windows within the broad band of parameter regime where the chaotic solution persists are identified and analysed. It is evident that the further transition from chaos to a high Rayleigh number periodic convection occurs via a period halving sequence of bifurcations.

Original languageEnglish (US)
Pages (from-to)69-91
Number of pages23
JournalTransport in Porous Media
Volume37
Issue number1
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

Keywords

  • Chaos
  • Free convection
  • Lorenz equations
  • Weak turbulence

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

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