Instability of convection in a fluid layer rotating about an oblique axis
Abstract
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 ψ, a stream function related to a largescale vertical vorticity field, we describe the instabilities of convection rolls. We show how the usual KüppersLortz instability, which leads to a continual precession of the roll pattern, can be suppressed by the oblique rotation vector. Of particular interest is the smallangle 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 smallamplitude rolls near the marginal stability boundary. A onedimensional instability leading to amplitudemodulated rolls is unaffected by the oblique rotation. Numerical simulations of the model equations are presented, which illustrate the instabilities analyzed.
 Publication:

Physical Review E
 Pub Date:
 January 2003
 DOI:
 10.1103/PhysRevE.67.016301
 Bibcode:
 2003PhRvE..67a6301P
 Keywords:

 47.54.+r;
 47.20.Bp;
 47.27.Te;
 47.20.Lz;
 Buoyancydriven instabilities;
 Secondary instabilities