• DOI:10.1103/PHYSREVE.67.016301
• Corpus ID: 10923494

Instability of convection in a fluid layer rotating about an oblique axis.

@article{Pollicott2003InstabilityOC,
  title={Instability of convection in a fluid layer rotating about an oblique axis.},
  author={S L Pollicott and P. C. Matthews and Stephen M. Cox},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2003},
  volume={67 1 Pt 2},
  pages={
          016301
        }
}

• S. Pollicott, P. Matthews, S. Cox
• Published 9 January 2003
• Physics, Environmental Science
• Physical review. E, Statistical, nonlinear, and soft matter physics

We analyze thermal convection in a fluid layer confined between isothermal horizontal boundaries at which the tangential component of the fluid stress vanishes. The layer rotates about an oblique, nearly vertical axis. Using a model set of equations for w, the horizontal planform of the vertical velocity component, and psi, a stream function related to a large-scale vertical vorticity field, we describe the instabilities of convection rolls. We show how the usual Küppers-Lortz instability, which leads to a continual precession of the roll pattern, can be suppressed by the oblique rotation vector. Of particular interest is the small-angle instability of rolls, to perturbations in the form of rolls that are almost aligned with the primary rolls; at finite Prandtl number, this instability is not prevented by the horizontal component of the rotation vector, unless this component is sufficiently strong, in which case stability is confined to small-amplitude rolls near the marginal stability boundary. A one-dimensional instability leading to amplitude-modulated rolls is unaffected by the oblique rotation. Numerical simulations of the model equations are presented, which illustrate the instabilities analyzed.