Large-scale circulation model for turbulent Rayleigh-Bénard convection

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Convection Phenomena

Background:

• Turbulent Rayleigh-Bénard convection is crucial in various natural and industrial processes.
• Understanding the large-scale circulation (LSC) dynamics, including its meandering and cessations, is key to predicting heat transport.
• Existing models often struggle to capture the complex, fluctuating behavior of LSC.

Purpose of the Study:

• To develop a physically motivated stochastic model for the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection.
• To simulate the meandering, rotation, and cessation dynamics of LSC in cylindrical samples.
• To compare model predictions with experimental measurements.

Main Methods:

• Formulation of a model based on two stochastic ordinary differential equations.
• One equation governs the strength of the LSC, while the other describes its azimuthal orientation.
• Stochastic forces are incorporated to phenomenologically represent turbulent fluctuations.

Main Results:

• The model successfully reproduces an azimuthally meandering LSC, consistent with experimental data.
• It captures occasional rotations of the LSC orientation.
• The model also simulates rare cessations of the LSC, with orientation changes uniformly distributed as observed in experiments.

Conclusions:

• The presented stochastic model provides a robust framework for understanding LSC in turbulent convection.
• It accurately captures key dynamic behaviors, including meandering, rotations, and cessations.
• The model's consistency with experimental findings validates its physical motivation and predictive capabilities.