Continuation and stability of convective modulated rotating waves in spherical shells

Area of Science:

• Fluid Dynamics
• Convection Dynamics
• Nonlinear Dynamics

Background:

• Thermal-Rossby waves emerge at the onset of convection in rotating spherical shells.
• Modulated rotating waves (MRW) are a complex phenomenon bifurcated from these initial waves.
• Understanding the stability of MRW is crucial for characterizing fluid behavior.

Purpose of the Study:

• To investigate the stability of modulated rotating waves (MRW).
• To identify regions of multistability in fluid convection.
• To classify bifurcations leading to complex flow patterns.

Main Methods:

• Newton-Krylov continuation techniques were employed.
• Equations of motion were analyzed in a rotating frame of reference.
• Nonslip boundary conditions and specific fluid parameters (E=10⁻⁴, Pr=0.1, η=0.35) were used.

Main Results:

• Unstable MRW, including those lacking azimuthal symmetry, were computed.
• Regions of multistability were identified.
• Tertiary Hopf bifurcations leading to three-frequency stable solutions were accurately determined.

Conclusions:

• Newton-Krylov continuation is effective for finding unstable MRW and regions of multistability.
• The stability analysis of MRW helps classify complex bifurcation sequences.
• The study accurately determined tertiary Hopf bifurcations in this system.