The spontaneous magnetic field direction in an anisotropic MHD dynamo

Shakhov, B. A.; Jurčišin, M.; Jurčišinová, E.; Stehlík, Milan

doi:10.3103/s0884591312050066

Cited by 3 publications

(1 citation statement)

References 29 publications

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“…Of course, in real systems, the linear regime quickly changes to a nonlinear one due to high growth rates, and dynamo generation can acquire more interesting features, see, e.g., [19]. The shell approach is rather useful for studying the questions of how a growing magnetic field affects the velocity field and what specific transformation of the velocity field changes and stops the generation process.Moreover, other dynamo approaches, for example, based on a field-theoretic renormalization group analysis also look no less promising and interesting for comparing of initial and nonlinear dynamo regimes [20][21][22]. However, in this paper we will not discuss these issues, restricting our consideration to the two initial simple questions: is it possible to relate the processes of small-scale generation in both models and which part of the Kolmogorov kinetic spectrum is responsible for the growth of magnetic energy.…”

Section: Introductionmentioning

confidence: 99%

Small-scale Kazantsev-Kraichnan dynamo in a MHD shell approach

Abushzada,

Yushkov,

Frick

et al. 2023

Phys. Scr.

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The small-scale magnetic energy generation in a turbulent velocity field is studied by two different approaches. One of them is based on the Kazantsev-Kraichnan model developed for turbulence with short-time velocity correlations, and the other uses the shell model of magnetohydrodynamic turbulence, describing the turbulent energy cascade on a finite number of spectral shells. We have found that the injection of weak magnetic field at the initial moment in both models leads to an exponential growth of magnetic energy and tried to determine whether these effects are of the same or different nature. The investigations have shown that the rates of growths and magnetic energy spectra in two approaches can be very much different, which can be attributed to the contradictions of the model assumptions and unknown correlation time. The discussion of these contradictions allows us to formulate a possible explanation, which is likely related to the fact that the small-scale magnetic field generation is under the influence of some spectral subrange, rather than the entire kinetic spectrum. Varying the correlation time of the velocity field and considering the spectral regions, we have determined the range of kinetic energy spectrum responsible for the small-scale dynamo generation.

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Section: Introductionmentioning

confidence: 99%

Small-scale Kazantsev-Kraichnan dynamo in a MHD shell approach

Abushzada,

Yushkov,

Frick

et al. 2023

Phys. Scr.

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Diffusion in anisotropic fully developed turbulence: Turbulent Prandtl number

Jurčišinová

Jurčišin

2016

Phys. Rev. E

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Using the field theoretic renormalization group technique in the leading order of approximation of a perturbation theory the influence of the uniaxial small-scale anisotropy on the turbulent Prandtl number in the framework of the model of a passively advected scalar field by the turbulent velocity field driven by the Navier-Stokes equation is investigated for spatial dimensions d>2. The influence of the presence of the uniaxial small-scale anisotropy in the model on the stability of the Kolmogorov scaling regime is briefly discussed. It is shown that with increasing of the value of the spatial dimension the region of stability of the scaling regime also increases. The regions of stability of the scaling regime are studied as functions of the anisotropy parameters for spatial dimensions d=3,4, and 5. The dependence of the turbulent Prandtl number on the anisotropy parameters is studied in detail for the most interesting three-dimensional case. It is shown that the anisotropy of turbulent systems can have a rather significant impact on the value of the turbulent Prandtl number, i.e., on the rate of the corresponding diffusion processes. In addition, the relevance of the so-called weak anisotropy limit results are briefly discussed, and it is shown that there exists a relatively large region of small absolute values of the anisotropy parameters where the results obtained in the framework of the weak anisotropy approximation are in very good agreement with results obtained in the framework of the model without any approximation. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly investigated for spatial dimensions d=4 and 5. It is shown that the dependence of the turbulent Prandtl number on the anisotropy parameters is very similar for all studied cases (d=3,4, and 5), although the numerical values of the corresponding turbulent Prandtl numbers are different.

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Simultaneous influence of helicity and compressibility on anomalous scaling of the magnetic field in the Kazantsev-Kraichnan model

2017

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Using the field theoretic renormalization group technique and the operator product expansion, the systematic investigation of the influence of the spatial parity violation on the anomalous scaling behavior of correlation functions of the weak passive magnetic field in the framework of the compressible Kazantsev-Kraichnan model with the presence of a large-scale anisotropy is performed up to the second order of the perturbation theory (two-loop approximation). The renormalization group analysis of the model is done and the two-loop explicit expressions for the anomalous and critical dimensions of the leading composite operators are found as functions of the helicity and compressibility parameters and their anisotropic hierarchies are discussed. It is shown that for arbitrary values of the helicity parameter and for physically acceptable (small enough) values of the compressibility parameter, the main role is played by the composite operators near the isotropic shell in accordance with the Kolmogorov's local isotropy restoration hypothesis. The anomalous dimensions of the relevant composite operators are then compared with the anomalous dimensions of the corresponding leading composite operators in the Kraichnan model of passively advected scalar field. The significant difference between these two sets of anomalous dimensions is discussed. The two-loop inertial-range scaling exponents of the single-time two-point correlation functions of the magnetic field are found and their dependence on the helicity and compressibility parameters is studied in detail. It is shown that while the presence of the helicity leads to more pronounced anomalous scaling for correlation functions of arbitrary order, the compressibility, in general, makes the anomalous scaling more pronounced in comparison to the incompressible case only for low-order correlation functions. The persistence of the anisotropy deep inside the inertial interval is investigated using the appropriate odd ratios of the correlation functions. It is shown that, in general, the persistence of the anisotropy is much more pronounced in the helical systems, while in the compressible turbulent environments this is true only for low-order odd ratios of the correlation functions.

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The spontaneous magnetic field direction in an anisotropic MHD dynamo

Cited by 3 publications

References 29 publications

Small-scale Kazantsev-Kraichnan dynamo in a MHD shell approach

Small-scale Kazantsev-Kraichnan dynamo in a MHD shell approach

Diffusion in anisotropic fully developed turbulence: Turbulent Prandtl number

Simultaneous influence of helicity and compressibility on anomalous scaling of the magnetic field in the Kazantsev-Kraichnan model

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