Clustering, chaos, and crisis in a bailout embedding map

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Chaos theory

Background:

• Inertial particles in fluid flows exhibit complex dynamics.
• Two-dimensional incompressible flows are fundamental in fluid mechanics.
• Dissipative maps can model complex dynamical systems.

Purpose of the Study:

• To investigate the dynamics of inertial particles in 2D incompressible flows.
• To model particle dynamics using four-dimensional dissipative bailout embedding maps.
• To analyze the phase diagram and dynamic behaviors in aerosol and bubble regimes.

Main Methods:

• Modeling particle dynamics with four-dimensional dissipative bailout embedding maps.
• Representing the base flow with 2D area-preserving maps.
• Analyzing the phase diagram and bifurcation diagrams of the embedding map.

Main Results:

• The embedding map exhibits periodic orbits, chaotic structures, and mixed regions in both aerosol and bubble regimes.
• An attractor merging and widening crisis was observed for aerosols, leading to a single chaotic attractor.
• Crisis-induced intermittency and power-law behavior were noted in aerosols, but not in bubbles.

Conclusions:

• The 4D dissipative embedding map effectively models diverse particle dynamics in different regimes.
• The study identifies specific parameter values for targeting periodic or chaotic behaviors.
• Findings have implications for understanding impurity dynamics in various applications.