Skip to main content
×
Home
    • Aa
    • Aa

On the stability of steady finite amplitude convection

  • A. Schlüter (a1), D. Lortz (a1) and F. Busse (a1)
Abstract

The static state of a horizontal layer of fluid heated from below may become unstable. If the layer is infinitely large in horizontal extent, the Boussinesq equations admit many different steady solutions. A systematic method is presented here which yields the finite-amplitude steady solutions by means of successive approximations. It turns out that not every solution of the linear problem is an approximation to the non-linear problem, yet there are still an infinite number of finite amplitude solutions. A similar procedure has been applied to the stability problem for these steady finite amplitude solutions with the result that three-dimensional solutions are unstable but there is a class of two-dimensional flows which are stable. The problem has been treated for both rigid and free boundaries.

Copyright
References
Hide All
Malkus, W. V. R.1954aProc. Roy. Soc. A, 225, 185.

Malkus, W. V. R.1954bProc. Roy. Soc. A, 225, 196.

Pellew, A. & Southwell, R. V.1940Proc. Roy. Soc. A, 176, 132.

Reid, W. H. & Harris, D. L.1958Phys. Fluids, 1, 102.

Segel, L.1965J. Fluid Mech.21, 359.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 72 *
Loading metrics...

Abstract views

Total abstract views: 227 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th October 2017. This data will be updated every 24 hours.