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Kazantsev dynamo in turbulent compressible flows.
Marco Martins Afonso1, Dhrubaditya Mitra2, Dario Vincenzi3
1Centro de Matemática (Faculdade de Ciências) da Universidade do Porto, Rua do Campo Alegre 687, Porto 4169-007, Portugal.
Proceedings. Mathematical, Physical, and Engineering Sciences
|April 23, 2019
Summary
This study explores the kinematic fluctuation dynamo in random flows, finding that increased compressibility generally slows magnetic field growth. However, specific flow conditions can unexpectedly enhance dynamo action, with a critical exponent of one for dynamo onset.
Area of Science:
- Astrophysics and Plasma Physics
- Fluid Dynamics
- Dynamo Theory
Background:
- The kinematic fluctuation dynamo problem investigates the generation of magnetic fields in turbulent flows.
- The Kazantsev model is a foundational study for understanding dynamo action in random flows.
- Compressibility effects in turbulent flows are crucial for understanding astrophysical and geophysical phenomena.
Purpose of the Study:
- To generalize the Kazantsev model by incorporating both solenoidal and potential flow components.
- To analyze the impact of flow compressibility and scaling exponents on magnetic field growth rates.
- To determine the critical conditions for dynamo action in these generalized random flows.
Main Methods:
- Mathematical modeling of random, white-in-time flows with solenoidal and potential components.
- Analysis of the kinematic dynamo equation under varying compressibility and scaling exponents.
- Investigating the dependence of magnetic field growth rates and critical magnetic Reynolds numbers on flow properties.
Main Results:
- Increased compressibility generally decreases magnetic field growth rates, but the dynamo effect persists.
- When scaling exponents differ (e.g., Kolmogorov and Burgers values), compressibility slows the dynamo less significantly.
- Cases exist where increased compressibility enhances magnetic field growth, particularly when the potential component is smoother.
- The critical scaling exponent for dynamo onset is consistently unity, independent of compressibility.
- Three-dimensional (d=3) flows exhibit unique behavior compared to other dimensions regarding critical exponents.
Conclusions:
- Flow compressibility plays a complex role in kinematic dynamo processes, with potential for enhancement under specific conditions.
- The critical exponent for dynamo action is robustly determined by flow properties, not compressibility.
- Dimensionality significantly influences dynamo behavior, with d=3 being a special case.
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