Simulations of astrophysical disks in the shearing box that are subject to the magnetorotational instability (MRI) show that activity appears to be reduced as the magnetic Prandtl number (Pm) is lowered. On the other hand, calculations for laboratory experiments show that saturation is achieved through modification of the background shear for Pm << 1. Guided by the results of calculations appropriate for laboratory experiments when Pm is very low, the axisymmetric stability of inviscid disturbances in a shearing box model immersed in a constant vertical background magnetic field is considered under a variety of shear profiles and boundary conditions in order to evaluate the hypothesis that modifications of the shear bring about saturation of the instability. It is found that the emergence and stability of the MRI is sensitive to the boundary conditions adopted. Channel modes do not appear to be stabilized through any modification of the background shear whose average remains Keplerian. However, systems that have non-penetrative boundaries can saturate the MRI through modification of the background shear. Conceptually equating the qualitative results from laboratory experiments to the conditions in a disk may therefore be misleading.
(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the fil…
Magnetorotational turbulence transports angular momentum in stratified disks with low magnetic Prandtl number but magnetic Reynolds number above a critical value
We extend the scaling relations of stably stratified turbulence from the geophysical regime of unity Prandtl number to the astrophysical regime of extremely small Prandtl number applicable to stably stratified regions of stars and gas giants. A transition to a new turbulent regime is found to occur when the Prandtl number drops below the inverse of the buoyancy Reynolds number, i.e. $PrRb<1$, which signals a shift of the dominant balance in the buoyancy equation. Application of critical balance arguments then derives new predictions for the anisotropic energy spectrum and dominant balance of t…
Small-scale dynamos are expected to operate in all astrophysical fluids that are turbulent and electrically conducting, for example the interstellar medium, stellar interiors, and accretion disks, where they may also be affected by or competing with large-scale dynamos. However, the possibility of small-scale dynamos being excited at small and intermediate ratios of viscosity to magnetic diffusivity (the magnetic Prandtl number) has been debated, and the possibility of them depending on the large-scale forcing wavenumber has been raised. Here we show, using four values of the forcing wavenumbe…
Small-scale dynamo saturation across magnetic Prandtl numbers using the EDQNM closure
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理中心）；Department of Physics, Ashoka University（阿肖卡大学物理系）
Convection in the Sun occurs at Rayleigh numbers, $Ra$, as high as $10^{22}$, molecular Prandtl numbers, $Pr$, as low as $10^{-6}$, under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of these extreme circumstances on turbulent heat transport are unknown, and no comparable conditions exist on Earth. Our goal is to understand how these effects scale (since we cannot yet replicate the Sun's conditions faithfully). We study thermal convection by using direct numerical simulations, and determine the variation with respect to $Pr$, to values as low a…
(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from …
We investigate sustenance and dependence on magnetic Prandtl number (${\rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual dir…
We consider the dynamics of a vertically stratified, horizontally-forced Kolmogorov flow. Motivated by astrophysical systems where the Prandtl number is often asymptotically small, our focus is the little-studied limit of high Reynolds number but low Péclet number (which is defined to be the product of the Reynolds number and the Prandtl number). Through a linear stability analysis, we demonstrate that the stability of two-dimensional modes to infinitesimal perturbations is independent of the stratification, whilst three-dimensional modes are always unstable in the limit of strong stratificati…
A concise review is given of astrophysically motivated experimental and theoretical research on Taylor-Couette flow. The flows of interest rotate differentially with inner cylinder faster than outer one but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as 10^6, hydrodynamic flows of this type (quasi-keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach…
By numerically solving the equations of rotating magnetohydrodynamics (MHD), the magnetic effect on dynamical tide is studied. It is found that magnetic field has a significant impact not only on the flow structure, i.e. the internal shear layers in rotating flow can be destroyed in the presence of a moderate or stronger magnetic field (in the sense that the Alfvén velocity is at least of the order of 0.1 of the surface rotational velocity), but also on the dispersion relation of waves excited by tidal force such that the range of tidal resonance is broadened by magnetic field. A major result …
We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two further types -- helically modified SMRI (H-SMRI) and helical MRI (HMRI) -- in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for upcoming large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main p…
Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $\approx 250$ were examined and multiple resolutions used for con…
Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: scaling properties and relation to upcoming DRESDYN-MRI experiment
