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On the stability of steady finite amplitude convection

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

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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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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