Magnetohydrodynamic instabilities in developed small-scale turbulence

Kleeorin, N.; Mond, M.; Rogachevskii, I.

doi:10.1063/1.860582

Cited by 47 publications

(54 citation statements)

References 5 publications

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“…Direct numerical simulations (DNS) of Brandenburg et al (2011a) have shown in surprising detail many aspects of NEMPI that were previously seen in mean-field simulations (MFS) of Brandenburg et al (2010) and that have been anticipated based on analytical studies for some time (Kleeorin et al 1989(Kleeorin et al , 1990(Kleeorin et al , 1993(Kleeorin et al , 1996Kleeorin & Rogachevskii 1994;Rogachevskii & Kleeorin 2007).…”

Section: Introductionmentioning

confidence: 99%

Competition of rotation and stratification in flux concentrations

Losada

Brandenburg

Kleeorin

et al. 2013

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Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the τ approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

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Section: Introductionmentioning

confidence: 99%

Competition of rotation and stratification in flux concentrations

Losada

Brandenburg

Kleeorin

et al. 2013

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“…Using the spectral τ approach, Kleeorin et al (1989Kleeorin et al ( , 1990) do indeed find this reversal of the sign of the total magnetic tension force. In addition, they find a reversal of the sign of the effective magnetic pressure term; see also Kleeorin & Rogachevskii (1994) and Kleeorin et al (1993Kleeorin et al ( , 1996. Rogachevskii & Kleeorin (2007) argue that, in a stratified medium, this can lead to the formation of large-scale magnetic flux structures and perhaps even sunspots -or at least active regions.…”

Section: Introductionmentioning

confidence: 99%

Properties of the negative effective magnetic pressure instability

et al. 2012

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As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter β characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β . The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

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“…This is quite the contrary of magnetic buoyancy, which is still expected to operate on the smaller scale of magnetic flux tubes and in the absence of turbulence. Both effects can lead to instability: the latter is the magnetic buoyancy or interchange instability (Newcomb 1961;Parker 1966), and the former is now often referred to as negative effective magnetic pressure instability (NEMPI), which has been studied at the level of mean-field theory for the past two decades (Kleeorin et al 1989(Kleeorin et al , 1990(Kleeorin et al , 1993(Kleeorin et al , 1996Kleeorin & Rogachevskii 1994;Rogachevskii & Kleeorin 2007). These are instabilities of a stratified continuous magnetic field, while the usual magnetic buoyancy instability requires nonuniform and initially separated horizontal magnetic flux tubes (Parker 1955;Spruit 1981;Schüssler et al 1994).…”

Section: Introductionmentioning

confidence: 99%

Magnetic flux concentrations in a polytropic atmosphere

Losada

Brandenburg

Kleeorin

2014

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Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods. To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MFS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results. Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the "potato-sack" effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field. Conclusions. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

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Magnetohydrodynamic instabilities in developed small-scale turbulence

Cited by 47 publications

References 5 publications

Competition of rotation and stratification in flux concentrations

Competition of rotation and stratification in flux concentrations

Properties of the negative effective magnetic pressure instability

Magnetic flux concentrations in a polytropic atmosphere

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