Thermal Rossby waves in a rotating annulus. Their stability

Area of Science:

• Fluid Dynamics
• Heat Transfer
• Nonlinear Dynamics

Background:

• Thermal convection in rotating systems is crucial for geophysical and astrophysical phenomena.
• Understanding nonlinear behavior, like rotating waves, is key to predicting complex fluid flows.
• The influence of system geometry (radius ratio) and rotation rate on convection stability requires detailed analysis.

Purpose of the Study:

• To numerically investigate nonlinear thermal convection in a fast rotating annulus with specific boundary conditions.
• To analyze the properties and stability of rotating waves emerging after a Hopf bifurcation.
• To classify coexisting solutions based on their relation to linear modes and study their stability across different parameters.

Main Methods:

• Numerical simulation of fluid flow in a rotating annulus.
• Analysis of nonlinear phenomena, including Hopf bifurcations and rotating waves.
• Parametric study varying radius ratio and rotation rate, focusing on stability regions.

Main Results:

• Coexistence of different solution types near the critical Rayleigh number, classified by their connection to linear modes.
• Stability of primary solutions is dependent on the radius ratio and rotation rate.
• Stability regions are highly sensitive to the radius ratio, particularly where the dominant mode changes.

Conclusions:

• The study elucidates the complex dynamics of rotating thermal convection, highlighting the interplay between rotation, geometry, and fluid properties.
• Rotating waves exhibit diverse behaviors and stability characteristics influenced by system parameters.
• Accurate prediction of convection stability requires careful consideration of the radius ratio's effect on dominant flow modes.