Stochastic Chaos in a Turbulent Swirling Flow

Area of Science:

• Fluid Dynamics
• Chaos Theory
• Nonlinear Dynamics

Background:

• Turbulent swirling flows exhibit complex dynamics.
• Understanding the transition to chaos in such systems is challenging.
• Low-dimensional modeling is sought for systems with high degrees of freedom.

Purpose of the Study:

• To provide experimental evidence for a random attractor in turbulent swirling flow.
• To model the turbulent attractor using stochastic Duffing equations.
• To demonstrate the utility of this model for systems with multiple quasistationary states.

Main Methods:

• Defining a global observable to track angular momentum flux asymmetry.
• Reconstructing the turbulent attractor from experimental data.
• Modeling the attractor using stochastic Duffing equations.
• Comparing model properties (quasistationary states, transition rates, Lyapunov exponents) with experimental data.

Main Results:

• Experimental evidence for a random attractor in turbulent swirling flow was obtained.
• Stochastic Duffing equations accurately modeled the experimental attractor's quantitative properties.
• Deterministic models and stochastic differential equations based on effective potentials failed to replicate key properties.
• The model successfully reproduced the number of quasistationary states, transition rates, effective dimensions, and Lyapunov exponent continuity.

Conclusions:

• The study demonstrates the existence and successful modeling of a random attractor in turbulent swirling flow.
• Stochastic Duffing equations provide a viable low-dimensional modeling approach for complex systems.
• Findings open new avenues for modeling systems with numerous degrees of freedom and multiple quasistationary states.