Sparse nonlinear models of chaotic electroconvection.

Area of Science:

• Fluid Dynamics and Chaos Theory
• Nonlinear Dynamics and Multiphysics Systems

Background:

• Convection, a key fluid transport phenomenon, is driven by gradients (thermal, electric).
• Existing convection models are often limited to simpler thermal systems.
• Chaos theory and reduced-order modeling have roots in convection modeling.

Purpose of the Study:

• To develop a reduced-order model for chaotic electroconvection at high electric Rayleigh numbers.
• To capture the complex three-way coupling between fluid, charge density, and electric fields.
• To simplify the dynamics of chaotic electroconvection for better understanding and application.

Main Methods:

• Extraction of coherent structures from charge density fields using Proper Orthogonal Decomposition (POD).
• Development of a nonlinear model for coherent structure dynamics via Sparse Identification of Nonlinear Dynamics (SINDy).
• Constraining the SINDy model to preserve symmetries of the original high-dimensional system.

Main Results:

• A reduced-order model successfully represents the dominant chaotic dynamics of electroconvection.
• The model effectively captures essential nonlinear interactions in the system.
• The developed model shows similarities to the Lorenz model but for a more complex system.

Conclusions:

• The study successfully created a simplified model for chaotic electroconvection.
• This reduced-order model provides insights into complex fluid-electric field interactions.
• The approach advances the modeling of multiphysics systems exhibiting chaotic behavior.