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Quantifying the tangling of trajectories using the topological entropy
S Candelaresi1, D I Pontin1, G Hornig1
1Division of Mathematics, University of Dundee, Dundee DD1 4HN, United Kingdom.
Chaos (Woodbury, N.Y.)
|October 2, 2017
Summary
We developed an efficient method to calculate topological entropy for fluid flows and magnetic fields. This technique uses material line stretching to quantify spatial variations in mixing efficiency.
Area of Science:
- Fluid dynamics
- Plasma physics
- Dynamical systems
Background:
- Topological entropy quantifies chaos in dynamical systems.
- Accurate computation is challenging for complex flows and fields.
- Existing methods struggle with high-resolution requirements.
Purpose of the Study:
- To develop an efficient computational method for topological entropy.
- To determine the spatial distribution of topological entropy.
- To analyze finite-time topological entropy variations.
Main Methods:
- Measuring the length of a material line in a flow.
- Adaptively increasing resolution at high-curvature locations.
- Utilizing computational fluid dynamics (CFD) principles.
Main Results:
- Successfully computed lower limits of topological entropy for 2D mappings.
- Demonstrated efficient computation of spatial entropy distribution.
- Showcased the ability to study unprecedented parameter regimes.
Conclusions:
- The method provides an efficient way to compute topological entropy and its spatial variations.
- This approach is applicable to 2D time-periodic fluid flows and 1D-periodic 3D magnetic fields.
- The results offer insights into braiding efficiency in practical applications.
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