scholarly journals DEPENDENCE OF THE SATURATION LEVEL OF MAGNETOROTATIONAL INSTABILITY ON GAS PRESSURE AND MAGNETIC PRANDTL NUMBER

2015 ◽  
Vol 808 (1) ◽  
pp. 54 ◽  
Author(s):  
Takashi Minoshima ◽  
Shigenobu Hirose ◽  
Takayoshi Sano
Keyword(s):  
Prandtl Number ◽  
Gas Pressure ◽  
Saturation Level ◽  
Magnetorotational Instability ◽  
Magnetic Prandtl Number

scholarly journals WKB thresholds of standard, helical, and azimuthal magnetorotational instability

2012 ◽  
Vol 8 (S290) ◽  
pp. 233-234 ◽  
Author(s):  
Oleg Kirillov ◽  
Frank Stefani
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Prandtl Number ◽  
Local Stability ◽  
Rotating Flows ◽  
Rossby Number ◽  
Magnetorotational Instability ◽  
Electrically Conducting ◽  
Magnetic Prandtl Number ◽  
Wavelength Approximation

AbstractWe consider rotating flows of an electrically conducting, viscous and resistive fluid in an external magnetic field with arbitrary combinations of axial and azimuthal components. Within the short-wavelength approximation, the local stability of the flow is studied with respect to perturbations of arbitrary azimuthal wavenumbers. In the limit of vanishing magnetic Prandtl number (Pm) we find that the maximum critical Rossby number (Ro) for the occurrence of the magnetorotational instability (MRI) is universally governed by the Liu limit ${\rm Ro}_{Liu}=2-2\sqrt{2}\approx -0.828$ which is below the value for Keplerian rotation RoKepler = −0.75.

scholarly journals Azimuthal magnetorotational instability with super-rotation

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
G. Rüdiger ◽  
M. Schultz ◽  
M. Gellert ◽  
F. Stefani
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Outer Cylinder ◽  
Magnetic Reynolds Number ◽  
Neutral Stability ◽  
Magnetorotational Instability ◽  
Magnetic Prandtl Number ◽  
The Stability

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

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).

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