scholarly journals Small-scale dynamos on the solar surface: dependence on magnetic Prandtl number

2015 ◽  
Vol 578 ◽  
pp. A54 ◽  
Author(s):  
I. Thaler ◽  
H. C. Spruit
Keyword(s):  
Prandtl Number ◽  
Solar Surface ◽  
Small Scale ◽  
Magnetic Prandtl Number

scholarly journals Critical Magnetic Prandtl Number for Small-Scale Dynamo

2004 ◽  
Vol 92 (5) ◽  
Author(s):  
Alexander A. Schekochihin ◽  
Steven C. Cowley ◽  
Jason L. Maron ◽  
James C. McWilliams
Keyword(s):  
Prandtl Number ◽  
Small Scale ◽  
Magnetic Prandtl Number

scholarly journals Hydromagnetic dynamos at the low Ekman and magnetic Prandtl numbers

2016 ◽  
Vol 46 (3) ◽  
pp. 221-244 ◽  
Author(s):  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Large Scale ◽  
Small Scale ◽  
Polar Regions ◽  
Magnetic Diffusion ◽  
Magnetic Prandtl Number ◽  
Prandtl Numbers ◽  
The Magnetic Field

Abstract Hydromagnetic dynamos are numerically investigated at low Prandtl, Ekman and magnetic Prandtl numbers using the PARODY dynamo code. In all the investigated cases, the generated magnetic fields are dominantly-dipolar. Convection is small-scale and columnar, while the magnetic field maintains its large-scale structure. In this study the generated magnetic field never becomes weak in the polar regions, neither at large magnetic Prandtl numbers (when the magnetic diffusion is weak), nor at low magnetic Prandtl numbers (when the magnetic diffusion is strong), which is a completely different situation to that observed in previous studies. As magnetic fields never become weak in the polar regions, then the magnetic field is always regenerated in the tangent cylinder. At both values of the magnetic Prandtl number, strong polar magnetic upwellings and weaker equatorial upwellings are observed. An occurrence of polar magnetic upwellings is coupled with a regenaration of magnetic fields inside the tangent cylinder and then with a not weakened intensity of magnetic fields in the polar regions. These new results indicate that inertia and viscosity are probably negligible at low Ekman numbers.

scholarly journals A multiscale dynamo model driven by quasi-geostrophic convection

2015 ◽  
Vol 780 ◽  
pp. 143-166 ◽  
Author(s):  
Michael A. Calkins ◽  
Keith Julien ◽  
Steven M. Tobias ◽  
Jonathan M. Aurnou
Keyword(s):  
Prandtl Number ◽  
Viscous Dissipation ◽  
Time Scale ◽  
Large Scale ◽  
Force Balance ◽  
Dynamo Model ◽  
Small Scale ◽  
Ohmic Dissipation ◽  
Evolution Time ◽  
Magnetic Prandtl Number

A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three time scales that respectively characterize the convective time scale, the large-scale magnetic evolution time scale and the large-scale thermal evolution time scale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large scale. For the order one magnetic Prandtl number model, the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the horizontal boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress & Soward (Phys. Rev. Lett., vol. 29, 1972, pp. 837–839), and provide a new theoretical framework for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.

scholarly journals Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence

2020 ◽  
Vol 636 ◽  
pp. A93 ◽  
Author(s):  
P. J. Käpylä ◽  
M. Rheinhardt ◽  
A. Brandenburg ◽  
M. J. Käpylä
Keyword(s):  
Magnetic Fields ◽  
Prandtl Number ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Scale Dependence ◽  
Scale Separation ◽  
Separation Ratio ◽  
Magnetic Prandtl Number ◽  
Magnetic Diffusivity ◽  
Forced Turbulence

Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results. We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function. Conclusions. The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9−0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4−0.8).

scholarly journals Small-Scale Solar Magnetic Fields

1976 ◽  
Vol 71 ◽  
pp. 69-99 ◽  
Author(s):  
J. O. Stenflo
Keyword(s):  
Magnetic Fields ◽  
Magnetic Flux ◽  
Solar Surface ◽  
Life Time ◽  
Wave Number ◽  
Small Scale ◽  
Solar Magnetic Fields ◽  
Field Amplification ◽  
Wave Numbers ◽  
Diffuse Form

The observed properties of small-scale solar magnetic fields are reviewed. Most of the magnetic flux in the photosphere is in the form of strong fields of about 100–200 mT (1–2 kG), which have remarkably similar properties regardless of whether they occur in active or quiet regions. These fields are associated with strong atmospheric heating. Flux concentrations decay at a rate of about 107 Wb s-1, independent of the amount of flux in the decaying structure. The decay occurs by smaller flux fragments breaking loose from the larger ones, i.e. a transfer of magnetic flux from smaller to larger Fourier wave numbers, into the wave-number regime where ohmic diffusion becomes significant. This takes place in a time-scale much shorter than the length of the solar cycle.The field amplification occurs mainly below the solar surface, since very little magnetic flux appears in diffuse form in the photosphere, and the life-time of the smallest flux elements is very short. The observations further suggest that most of the magnetic flux in quiet regions is supplied directly from below the solar surface rather than being the result of turbulent diffusion of active-region magnetic fields.

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