Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits.

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Chaos Theory

Background:

• Turbulent flows are complex and often appear chaotic.
• Understanding the underlying dynamics of turbulence is a major challenge in physics.

Purpose of the Study:

• To identify and validate the dynamical relevance of unstable periodic orbits (UPOs) in turbulent flows.
• To investigate the statistical significance of UPOs in quasi-two-dimensional turbulent systems.

Main Methods:

• Laboratory experiments and numerical simulations of quasi-two-dimensional turbulent flow.
• Computation and analysis of unstable time-periodic solutions (UPOs).
• Validation of UPOs by observing transient dynamics in turbulent flows.

Main Results:

• Clear signatures of unstable time-periodic solutions were observed in moderately turbulent quasi-two-dimensional flow.
• Turbulent flows were shown to transiently shadow these UPOs in both experiments and simulations.
• Computed UPOs were statistically significant, with turbulent flows frequently visiting states near these orbits.
• Average energy input and dissipation rates for turbulent flow and visited UPOs differed by only a few percent.

Conclusions:

• Unstable periodic orbits play a dynamically relevant role in the behavior of turbulent flows.
• Turbulent dynamics can be understood as a transient shadowing of these underlying UPOs.
• The statistical significance and energetic similarity suggest UPOs are fundamental to understanding turbulent energy transfer.