Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

Sotos Generalis, Kaoru Fujimura

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.
Original languageEnglish
Article number084401
Number of pages11
JournalJournal of Physical Society of Japan
Volume78
Issue number8
DOIs
Publication statusPublished - 10 Aug 2009
Event5th European thermal sciences conference - Eindhoven, Netherlands
Duration: 18 May 200822 May 2008
http://www.eurotherm2008.tue.nl/

Keywords

  • equilibrium states
  • periodic finite amplitude flow
  • horizontal channel
  • differential heating
  • rigid boundaries
  • Navier-Stokes equations
  • Landau coefficients
  • Newton-Raphson iterative method
  • Fourier expansion
  • Prandtl numbers

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