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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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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