Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Geophysics and Astrophysics

Background:

• Turbulent Rayleigh-Bénard convection exhibits complex dynamics, including boundary layer oscillations.
• Massive thermal plume eruptions and circulation reversals are observed in geophysical and astrophysical convection systems.

Purpose of the Study:

• To model dynamic instabilities in coupled nonlinear delay differential equations for turbulent Rayleigh-Bénard convection.
• To understand the origin of rare massive eruptions and flow pattern changes in convection systems.

Main Methods:

• Analysis of two coupled nonlinear delay differential equations.
• Introduction of sensitivity parameters for top and bottom boundary layer instabilities.
• Identification of in-phase single-period, multi-period, and chaotic solutions.

Main Results:

• Three solution types were identified: in-phase single-period oscillations, multi-period oscillations, and chaos.
• Chaotic solutions exhibit rare, large-amplitude fluctuations.
• Statistical properties of fluctuations match experimental observations of thermal plume eruptions.

Conclusions:

• The study provides insights into the mechanisms driving massive thermal plume eruptions.
• The model explains random reversals of large-scale circulation in turbulent convection.
• Findings offer new perspectives on phenomena in geophysical and astrophysical convection systems.