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

Sotos C. Generalis, Kaoru Fujimura

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel 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 coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.
Original languageEnglish
Title of host publicationProceedings 5th European Thermal-Sciences Conference
EditorsG.G.M. Stoffels, T.H. van der Meer, A.A. van Steenhoven
Place of PublicationEindhoven (NL)
PublisherEindhoven University of Technology
PagesNCV_2
ISBN (Print)9789038612744
Publication statusPublished - May 2008

Fingerprint

convective flow
Rayleigh number
Prandtl number
Navier-Stokes equation
newton
convection
disturbances
perturbation
heating
expansion
thresholds
coefficients

Bibliographical note

5th European Thermal-Sciences Conference, 18-21 May 2008, Eindhoven (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

Cite this

Generalis, S. C., & Fujimura, K. (2008). Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. In G. G. M. Stoffels, T. H. van der Meer, & A. A. van Steenhoven (Eds.), Proceedings 5th European Thermal-Sciences Conference (pp. NCV_2). Eindhoven (NL): Eindhoven University of Technology.
Generalis, Sotos C. ; Fujimura, Kaoru. / Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. Proceedings 5th European Thermal-Sciences Conference. editor / G.G.M. Stoffels ; T.H. van der Meer ; A.A. van Steenhoven. Eindhoven (NL) : Eindhoven University of Technology, 2008. pp. NCV_2
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Generalis, SC & Fujimura, K 2008, Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. in GGM Stoffels, TH van der Meer & AA van Steenhoven (eds), Proceedings 5th European Thermal-Sciences Conference. Eindhoven University of Technology, Eindhoven (NL), pp. NCV_2.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. / Generalis, Sotos C.; Fujimura, Kaoru.

Proceedings 5th European Thermal-Sciences Conference. ed. / G.G.M. Stoffels; T.H. van der Meer; A.A. van Steenhoven. Eindhoven (NL) : Eindhoven University of Technology, 2008. p. NCV_2.

Research output: Chapter in Book/Report/Conference proceedingChapter

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T1 - Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

AU - Generalis, Sotos C.

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N2 - In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel 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 coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

AB - In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel 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 coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

KW - equilibrium states

KW - periodic finite amplitude flow

KW - horizontal channel

KW - differential heating

KW - rigid boundaries

KW - Navier-Stokes equations

KW - Landau coefficients

KW - Newton-Raphson iterative method

KW - Fourier expansion

KW - Prandtl numbers

M3 - Chapter

SN - 9789038612744

SP - NCV_2

BT - Proceedings 5th European Thermal-Sciences Conference

A2 - Stoffels, G.G.M.

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A2 - van Steenhoven, A.A.

PB - Eindhoven University of Technology

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Generalis SC, Fujimura K. Range of validity of weakly non-linear theory in Rayleigh-Bénard convection. In Stoffels GGM, van der Meer TH, van Steenhoven AA, editors, Proceedings 5th European Thermal-Sciences Conference. Eindhoven (NL): Eindhoven University of Technology. 2008. p. NCV_2