Skip to main content
SpringerLink
Log in

Thermocapillar and thermogravitatory waves in a convection problem

  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

We study, from a numerical point of view, a thermal convection problem in a cylindrical annulus where a dynamic flow is imposed through a non-zero temperature gradient at the bottom. Experimentally, many interesting dynamical behaviours have been discovered in this system, which are controlled by heat related parameters and buoyant and thermocapillary instability mechanisms. By setting the Marangoni or the Rayleigh numbers equal to zero we explore the origin of different stationary, oscillatory, and codimension two stationary-oscillatory structures and their connection to either thermocapillary or thermogravitatory effects. We find that waves are possible in both cases if heat related parameters are conveniently tuned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bénard, H.: Les tourbillons cellulaires dans une nappe liquide. Rev. Gén. Sci. Pures Appl. 11, 1261–1268 (1900)

  2. Bernardi, C., Maday, Y.: Approximations spectrales de problemes aux limites elliptiques. Springer-Verlag, Berlin (1991)

  3. Burguete, J., Mokolobwiez, N., Daviaud, F., Garnier, N., Chiffaudel, A.: Buoyant-thermocapillary instabilities in extended layers subjected to a horizontal temperature gradient. Phys. Fluids 13, 2773–2787 (2001)

  4. Daviaud, F., Vince, J.M.: Traveling waves in afluid layer subjected to a horizontal temperature gradient. Phys. Rev. E 48, 4432–4436 (1993)

  5. Ezersky, A.B., Garcimartín, A., Burguete, J., Mancini, H.L., Pérez-García, C.: Hydrothermal waves in Marangoni convection in a cylindrical container. Phys. Rev. E 47, 1126–1131 (1993)

  6. Garnier, N.: Ondes non-linéaires a une et deux dimensions dans une mince couche de fluide. Thesis, Uni. Paris 7, Denis Diderot (2000)

  7. Garnier, N., Chiffaudel, A.: Two dimensional hydrothermal waves in an extended cylindrical vessel. Eur. Phys. J. B 19, 87–95 (2001)

  8. Herrero, H., Mancho, A.M.: Influence of aspect ratio in convection due to non-uniform heating. Phys. Rev E 57, 7336–7339 (1998)

  9. Herrero, H., Mancho, A.M.: On pressure boundary conditions for thermoconvective problems. Int. J. Numer. Meth. Fluids 39, 391–402 (2002)

  10. Hoyas, S., Herrero, H., Mancho, A.M.: Estudio numérico de un problema de convección en un dominio cilíndrico. CD Actas del XVII CEDYA/VII CMA (2001)

  11. Hoyas, S., Herrero, H., Mancho, A.M.: Thermal convection in a cylindrical annulus heated laterally. J. Phys. A: Math and Gen. 35, 4067–4083 (2002)

  12. Hoyas, S., Herrero, H., Mancho, A.M.: Bifurcation diversity of dynamic thermocapillary liquid layers. Phys. Rev. E, 66, 057301 (2002)

  13. Hoyas, S.: Estudio teórico y numérico de un problema de convección de Bénard-Marangoni. Tesis, Universidad Complutense de Madrid (2003)

  14. Hoyas, S., Mancho, A.M., Herrero, H., Garnier, N., Chiffaudel, A.: Bénard-Marangoni convection in a differentially heated cylindrical cavity. Submitted to Phys. Fluids

  15. Mancho, A.M., Herrero, H., Burguete, J.: Primary instabilities in convective cells due to non-uniform heating. Phys. Rev E 56, 2916–2923 (1997)

  16. Mancho, A.M., Herrero, H.: Instabilities in a lateraly heated liquid layer. Phys. Fluids 12, 1044–1051 (2000)

  17. Mercier, J.F., Normand, C.: Buoyant-thermocapillary instabilities of differentially heated liquid layers. Phys. Fluids 8, 1433–1445 (1996)

  18. Pelacho, M.A., Burguete, J.: Temperature oscillations of hydrothermal waves in thermocapillary-buoyancy convection. Phys. Rev. E 59, 835–840 (1999)

  19. Riley, R.J., Neitzel, G.P.: Instability of thermocapillary-buoyancy convection in shallow layers. Part 1. Characterization os steady and oscillatory instabilities. J. Fluid Mech 359, 143–164 (1998)

  20. Smith, M.K., Davis, S.H.: Instabilities of dynamic thermocapillary layers. 1. Convective instabilities. J. Fluid Mech. 132, 119–144 (1983)

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias Químicas, Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain

    S. Hoyas & H. Herrero

  2. Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

    A.M. Mancho

Authors
  1. S. Hoyas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Herrero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A.M. Mancho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Herrero.

Additional information

Communicated by

H.J.S. Fernando

PACS

47.27.Te, 02.60.Cb, 47.20.y

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoyas, S., Herrero, H. & Mancho, A. Thermocapillar and thermogravitatory waves in a convection problem. Theor. Comput. Fluid Dyn. 18, 309–321 (2004). https://doi.org/10.1007/s00162-004-0143-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-004-0143-3

Keywords

Search

Navigation