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Published on: February 3, 2014
Chaotic advection in compressible helical flow
V N Govorukhin1, A Morgulis, V I Yudovich
1Department of Mathematics and Mechanics, Rostov State University, 5 Zorge Street, Rostov-na-Donu 344104, Russia.
Summary
Spatially dependent helicity in compressible helical flow significantly enhances chaotic dynamics and mixing. This study introduces a Hamiltonian formulation, revealing why this flow is more chaotic than incompressible variants.
Area of Science:
- Fluid dynamics
- Chaos theory
- Mathematical physics
Background:
- Compressible helical flow with non-zero divergence (div v ≠ 0) exhibits complex dynamics.
- Helicity, a key parameter, influences chaotic behavior and mixing efficiency.
- Understanding the transition to chaotic dynamics in such flows is crucial.
Purpose of the Study:
- To investigate the impact of spatially dependent helicity on chaotic dynamics in compressible helical flow.
- To develop a Hamiltonian formulation for analyzing these systems.
- To elucidate the enhanced chaotic properties compared to incompressible flows.
Main Methods:
- Incorporation of density dependence into new variables for Hamiltonian formulation.
- Application of Kolmogorov-Arnold-Moser (KAM) theory.
- Numerical simulations of an ABC flow analog.
Main Results:
- Spatially dependent helicity drastically increases the area of chaotic dynamics and mixing.
- A Hamiltonian formulation was achieved by incorporating density dependence.
- Simulations confirmed that compressible helical flow is "more chaotic" than incompressible flow.
- A novel dynamical system with "dense" island chains was described.
Conclusions:
- Compressible helical flow with spatially dependent helicity offers enhanced mixing and chaotic dynamics.
- The Hamiltonian formulation provides a theoretical framework for understanding these properties.
- The findings offer insights into the fundamental differences in chaotic behavior between compressible and incompressible helical flows.
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