Skip to main content
Log in

Bounding flows for turbulent convection

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.


  1. Busse, F. H., Bounds on the transport of mass and momentum by turbulent flow between parallel plates. Z. angew. Math. Phys. 20, 1–14 (1969).

    Google Scholar 

  2. Busse, F. H., On Howard's upper bound for heat transport in turbulent convection. J. Fluid Mech. 37, 457–477 (1969).

    Google Scholar 

  3. Busse, F. H., & D. D. Joseph, Bounds for heat transport in a porous layer. J. Fluid Mech. 54, 521–544 (1972).

    Google Scholar 

  4. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability. Oxford 1961.

  5. Friedman, A., Partial Differential Equations. New York 1969.

  6. Gupta, V. P., & D. D. Joseph, Bounds for heat transport in a porous layer. To be published.

  7. Howard, L., Heat transport by turbulent convection. J. Fluid Mech. 17, 405–432 (1963).

    Google Scholar 

  8. Howard, L., Bounds on flow quantities. Ann. Rev. of Fluid Mech. 4, 473–494 (1972).

    Google Scholar 

  9. Lapwood, E. R., Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44, 508–521 (1948).

    Google Scholar 

  10. Malkus, W. V. R., Discrete transitions in turbulent convection. Proc. Roy. Soc. A. 225, 185–195 (1954a).

    Google Scholar 

  11. Vainberg, M. M., Le Problème de la Minimisation des Fonctionnelles Non Linéaires, in Problems in Non-Linear Analysis. C.I.M.E. 1970. Edizioni Cremonese.

Download references

Author information

Authors and Affiliations


Additional information

Communicated by D. D. Joseph

The preparation of this paper was supported in part by a grant from the U.S. National Science Foundation, Number G.P. 29273.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Auchmuty, J.F.G. Bounding flows for turbulent convection. Arch. Rational Mech. Anal. 51, 228–238 (1973).

Download citation

  • Received:

  • Issue Date:

  • DOI: