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- Brandenburg, Axel, et al.
(författare)
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Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field
- 2014
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 562
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Tidskriftsartikel (refereegranskat)abstract
- Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims. We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods. We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results. Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about eight density scale heights. Despite being <= 1% equipartition strength, it is important that their lower part is included within the computational domain to achieve the full strength of the instability. Conclusions. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated. Application to sunspots remains a viable possibility.
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| 2. |
- Jabbari, Sarah, et al.
(författare)
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Magnetic flux concentrations from dynamo-generated fields
- 2014
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 568
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Tidskriftsartikel (refereegranskat)abstract
- Context The mean field theory of magnetized stellar convection gives rise to two distinct instabilities; the large-scale dynamo instability, operating in the bulk of the convection zone and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation. However, as follows from theoretical analysis, the growth rate of NEMPI is suppressed with increasing rotation rates. On the other hand, recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. Aims. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha(2) mean field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. Methods. We use both DNS and mean field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal held, We use the test-field method to compute relevant dynamo coefficients. Results. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively reproduced with MPS. As expected for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Conclusions. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over For the solar rotation rate, the corresponding turbulent turnover time is about 5 h, with dynamo action commencing in the layers beneath.
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| 3. |
- JABBARI, SARAH, 1981-
(författare)
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Origin of solar surface activity and sunspots
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the last few years, there has been significant progress in the development of a new model for explaining magnetic flux concentrations, by invoking the negative effective magnetic pressure instability (NEMPI) in a highly stratified turbulent plasma. According to this model, the suppression of the turbulent pressure by a large-scale magnetic field leads to a negative contribution of turbulence to the effective magnetic pressure (the sum of non-turbulent and turbulent contributions). For large magnetic Reynolds numbers the negative turbulence contribution is large enough, so that the effective magnetic pressure is negative, which causes a large-scale instability (NEMPI). One of the potential applications of NEMPI is to explain the formation of active regions on the solar surface. On the other hand, the solar dynamo is known to be responsible for generating large-scale magnetic field in the Sun. Therefore, one step toward developing a more realistic model is to study a system where NEMPI is excited from a dynamo-generated magnetic field. In this context, the excitation of NEMPI in spherical geometry was studied here from a mean- field dynamo that generates the background magnetic field. Previous studies have shown that for NEMPI to work, the background field can neither be too weak nor too strong. To satisfy this condition for the dynamo-generated magnetic field, we adopt an “alpha squared dynamo” with an α effect proportional to the cosine of latitude and taking into account alpha quenching. We performed these mean-field simulations (MFS) using the Pencil Code. The results show that dynamo and NEMPI can work at the same time such that they become a coupled system. This coupled system has then been studied separately in more detail in plane geometry where we used both mean-field simulations and direct numerical simulations (DNS).Losada et al. (2013) showed that rotation suppresses NEMPI. However, we now find that for higher Coriolis numbers, the growth rate increase again. This implies that there is another source that provides the excitation of an instability. This mechanism acts at the same time as NEMPI or even after NEMPI was suppressed. One possibility is that for higher Coriolis numbers, an α2 dynamo is activated and causes the observed growth rate. In other words, for large values of the Coriolis numbers we again deal with the coupled system of NEMPI and mean-field dynamo. Both, MFS and DNS confirm this assumption. Using the test-field method, we also calculated the dynamo coefficients for such a system which again gave results consistent with previous studies. There was a small difference though, which is interpreted as being due to the larger scale separation that we have used in our simulations.Another important finding related to NEMPI was the result of Brandenburg et al. (2013), that in the presence of a vertical magnetic field NEMPI results in magnetic flux concentrations of equipartition field strength. This leads to the formation of a magnetic spot. This finding stimulated us to investigate properties of NEMPI for imposed vertical fields in more detail. We used MFS and DNS together with implicit large eddy simulations (ILES) to confirm that an initially uniform weak vertical magnetic field will lead to a circular magnetic spot of equipartition field strength if the plasma is highly stratified and scale separation is large enough. We determined the parameter ranges for NEMPI for a vertical imposed field. Our results show that, as we change the magnitude of the vertical imposed field, the growth rate and geometry of the flux concentrations is unchanged, but their position changes. In particular, by increasing the imposed field strength, the magnetic concentration forms deeper down in the domain.
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