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pure and applied geophysics

, Volume 117, Issue 5, pp 958–987 | Cite as

An approximate method for determining the stability of two-scale flow in the mantle

  • John N. Skilbeck
  • P. Dan McKenzie
Article

Summary

An approximate method of calculating the stability of two-dimensional convection rolls to cross-roll disturbances is evaluated by comparison with the results from exact analyses and good agreement is obtained. In particular, investigation of the second mode of the disturbance provides a qualitative estimate of the terms excluded in making the approximation. We conclude that this approximate method, sensibly used, gives a good indication of the stability of rolls to cross-roll disturbances.

Application of this method is made to convection rolls heated partially or wholly from within, and to rolls in the presence of a longitudinal shear flow. The approximation indicates that, at high Rayleigh Numbers, growth rates are underestimated and so the amount of shear calculated to stabilise longitudinal rolls is a lower bound. Our results suggest that two-dimensional rolls are unlikely to be a stable flow pattern beneath even the fastest moving plates.

Key words

Mantle convection Plate tectonics 

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Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • John N. Skilbeck
    • 1
  • P. Dan McKenzie
    • 2
  1. 1.Department of Geological SciencesDurhamU.K.
  2. 2.Department of Geodesy and GeophysicsCambridge

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