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Related Experiment Video

Updated: Jul 6, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Shear-induced chaos in nonlinear Maxwell-model fluids.

Chris Goddard¹, Ortwin Hess, Alexander G Balanov

¹Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, GU2 7XH, United Kingdom. c.goddard@surrey.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 21, 2008

Summary

This study explores complex fluid dynamics in non-Newtonian fluids, revealing nonlinear responses and deterministic chaos under specific flow conditions. Researchers mapped chaotic behaviors using Lyapunov exponents and bifurcation analysis, identifying key stability loss mechanisms.

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Area of Science:

Fluid Dynamics
Non-Newtonian Fluid Mechanics
Chaos Theory

Background:

Non-Newtonian fluids exhibit complex stress tensor behavior.
Understanding their dynamics is crucial for various industrial applications.
Previous models often simplify these complex responses.

Purpose of the Study:

To investigate a generalized model for stress tensor behavior in non-Newtonian fluids.
To analyze nonlinear responses and deterministic chaos in plane Couette flow.
To identify parameters and mechanisms driving complex fluid dynamics.

Main Methods:

Utilized a generalized model for stress tensor analysis.
Simulated spatially homogeneous plane Couette flow.
Employed largest Lyapunov exponent for chaos mapping.
Conducted bifurcation diagrams and stability analysis.

Main Results:

Observed a variety of nonlinear responses and deterministic chaos.
Identified shear rate and temperature/density as key parameters influencing chaos.
Revealed rich dynamics through bifurcation and stability analyses.
Identified Hopf, saddle-node, and period-doubling bifurcations as stability loss mechanisms.

Conclusions:

The generalized model effectively captures complex dynamics in non-Newtonian fluids.
Nonlinear responses and chaos are inherent in these systems under specific conditions.
Bifurcation analysis provides insights into the transition to chaotic behavior.