Geometry effects on Rayleigh-Bénard convection in rotating annular layers

Area of Science:

• Fluid Dynamics
• Convective Heat Transfer
• Nonlinear Dynamics

Background:

• Rayleigh-Bénard convection is a fundamental mode of heat transport.
• Rotating systems introduce Coriolis forces, altering convection patterns.
• Annular cavities create geometric confinement and curvature effects.

Purpose of the Study:

• To investigate the onset of convection in rotating annular cavities.
• To analyze the influence of curvature and confinement on sidewall convection.
• To understand the transition from traveling waves to steady patterns.

Main Methods:

• Three-dimensional spectral solutions of the Oberbeck-Boussinesq equations.
• Numerical simulation of fluid flow in a rotating annular cavity.
• Analysis of sidewall convection onset and pattern formation.

Main Results:

• Convection initiates as azimuthal traveling waves at sidewalls, below critical Rayleigh number for infinite layers.
• Outer boundary curvature promotes sidewall mode onset; inner boundary curvature delays it.
• Increased radial confinement leads to interaction and merging of traveling waves into steady patterns.

Conclusions:

• Geometric factors (curvature, confinement) significantly impact convection onset in rotating annular cavities.
• Sidewall convection is a distinct phenomenon influenced by boundary geometry.
• The study elucidates pattern selection mechanisms in confined rotating flows.