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 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physical review. E, Statistical, nonlinear, and soft matter physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.