Effective control of complex turbulent dynamical systems through statistical functionals.

Area of Science:

• Complex Systems Science
• Fluid Dynamics
• Statistical Mechanics

Background:

• Turbulent dynamical systems with high-dimensional phase spaces and numerous instabilities are prevalent across science and engineering.
• Controlling these systems, such as in climate change mitigation or turbulent flow management, presents a significant challenge.
• Existing control methods are insufficient for complex turbulent systems due to interacting instabilities.

Purpose of the Study:

• To propose an effective statistical control strategy for complex turbulent dynamical systems.
• To address the challenge of controlling systems with a large number of interacting instabilities.
• To leverage recent advancements in statistical energy principles and linear response theory.

Main Methods:

• Development of a statistical control strategy based on a statistical energy principle.
• Application of statistical linear response theory for control design.
• Verification of the strategy on the 40D Lorenz 1996 model under various turbulent regimes.

Main Results:

• The proposed statistical control strategy demonstrates practical efficiency.
• The control method is verified on a high-dimensional turbulent model (40D Lorenz 1996).
• The strategy is effective even when a significant portion of the phase space is unstable.

Conclusions:

• The developed statistical control strategy offers a viable approach for managing complex turbulent systems.
• This method provides a new paradigm for controlling systems where traditional methods fail.
• The findings have implications for climate science, material science, and neural science applications.