Dynamical effects of the ambipolar diffusion in a protoplanetary disc

2020 ◽  
Vol 497 (2) ◽  
pp. 1634-1653 ◽  
Author(s):  
Mahmoud Gholipour
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Outer Region ◽  
Ambipolar Diffusion ◽  
The Self ◽  
Mhd Equations ◽  
Solution Technique ◽  
Self Similar

ABSTRACT Several recent simulation works in the non-ideal magnetohydrodynamic (MHD) formalism have shown the importance of ambipolar diffusion (AD) within the protoplanetary discs (PPDs) at large radii. In this study, we model the time evolution of a polytropic PPD in the presence of the AD. In this regard, the non-ideal MHD equations are investigated in the outer region of a PPD where the magnetic field evolution is dominated by the AD. The self-similar solution technique is used for a polytropic fluid including the self-gravity and viscosity. The ambipolar diffusivity and its derivative are crucial for the formulation of this study. Hence, this variable is scaled by an important factor, that is the Elsasser number. The self-similar equations are derived, and the semi-analytical and numerical solutions are presented for the isothermal and polytropic cases. The analytical approach enables us to know the asymptotic behaviour of the physical variables in a PPD, such as the angular momentum and magnetic field. Furthermore, the coupling/decoupling of magnetic field with the angular momentum was discussed analytically to find a corresponding model for the angular momentum loss at large radii of a PPD. Regarding this approach, we found that the magnetic braking induced by the AD at large radii has a high potential to loss the angular momentum even if the turbulent viscosity is not efficient. Also, the sign and values of vertical velocity strongly depends on the sign and values of radial field in the polytropic case.

Annular self-similar solutions in ideal magnetogasdynamics

2008 ◽  
Vol 74 (4) ◽  
pp. 531-554 ◽  
Author(s):  
R. M. LOCK ◽  
A. J. MESTEL
Keyword(s):  
Magnetic Field ◽  
Initial Value Problem ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
The Self ◽  
Initial Value ◽  
Azimuthal Magnetic Field ◽  
Self Similar ◽  
Similar Solutions ◽  
Z Pinch

AbstractWe consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

scholarly journals Magnetized Accretion Disks Driving Jets

1994 ◽  
Vol 159 ◽  
pp. 249-252
Author(s):  
G. Pelletier ◽  
J. Ferreira ◽  
F. Rosso
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Accretion Disk ◽  
Accretion Disks ◽  
The Self ◽  
Mhd Equations ◽  
Back Reaction ◽  
Systematic Method ◽  
Field Lines

In this brief communication, we present some progress in the investigation of a most promising model that was designed to combine ejection with accretion. In this model, a bipolar configuration of opened magnetic field lines that thread the accretion disk, allows the extraction of angular momentum, the acceleration of matter up to super Alfvénic velocities and the self collimation of the jet. However, important issues have remained unsolved. First, a systematic method for solving the jet MHD equations with their critical surfaces was lacking. Second, the capability of accretion disks to generate super Alfvénic jets was unknown. Third, the back-reaction of the ejection on the accretion disk dynamics and its energetics remained to be done. Solving these three points led us to draw some noteworthy consequences for the understanding of AGNs.

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

scholarly journals ACCRETION AND PLASMA OUTFLOW FROM DISSIPATIONLESS DISCS

2010 ◽  
Vol 19 (03) ◽  
pp. 339-365 ◽  
Author(s):  
S. V. BOGOVALOV ◽  
S. R. KELNER
Keyword(s):  
Angular Momentum ◽  
Similar Case ◽  
Gravitational Energy ◽  
Accretion Disc ◽  
The Self ◽  
Low Viscosity ◽  
Variable Polarity ◽  
Self Similar ◽  
Similar Solutions ◽  
High Electric Conductivity

We consider the specific case of disc accretion for negligibly low viscosity and infinitely high electric conductivity. The key component in this model is the outflowing magnetized wind from the accretion disc, since this wind effectively carries away angular momentum of the accreting matter. Assuming magnetic field has variable polarity in the disc (to avoid magnetic flux and energy accumulation at the gravitational center), this leads to radiatively inefficient accretion of the disc matter onto the gravitational center. In such a case, the wind forms an outflow, which carries away all the energy and angular momentum of the accreted matter. Interestingly, in this framework, the basic properties of the outflow (as well as angular momentum and energy flux per particle in the outflow) do not depend on the structure of accretion disc. The self-similar solutions obtained prove the existence of such an accreting regime. In the self-similar case, the disc accretion rate (Ṁ) depends on the distance to the gravitational center, r, as [Formula: see text], where λ is the dimensionless Alfvenic radius. Thus, the outflow predominantly occurs from the very central part of the disc provided that λ ≫ 1 (it follows from the conservation of matter). The accretion/outflow mechanism provides transformation of the gravitational energy from the accreted matter into the energy of the outflowing wind with efficiency close to 100%. The flow velocity can essentially exceed the Kepler velocity at the site of the wind launch.

Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions

2003 ◽  
Vol 125 (6) ◽  
pp. 952-962 ◽  
Author(s):  
C. Midya ◽  
G. C. Layek ◽  
A. S. Gupta ◽  
T. Ray Mahapatra
Keyword(s):  
Magnetic Field ◽  
Flow Separation ◽  
Separation Zone ◽  
Transverse Magnetic ◽  
Mhd Equations ◽  
Staggered Grid ◽  
Solution Technique ◽  
Computational Domain ◽  
Pressure Poisson Equation ◽  
The Magnetic Field

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically. It is found that the flow separates downstream of the constriction. With increase in the magnetic field, the flow separation zone diminishes in size and for large magnetic field, the separation zone disappears completely. Wall shear stress increases with increase in the magnetic field strength. It is also found that for symmetrically situated constrictions on the channel walls, the critical Reynolds number for the flow bifurcation (i.e., flow asymmetry) increases with increase in the magnetic field.

Numerical study of toroidal magnetic field on the self-gravitating protoplanetary disks

2020 ◽  
Vol 29 (09) ◽  
pp. 2050067
Author(s):  
Hanifeh Ghanbarnejad ◽  
Maryam Ghasemnezhad
Keyword(s):  
Magnetic Field ◽  
Accretion Disks ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Ohmic Heating ◽  
The Self ◽  
Toroidal Magnetic Field ◽  
Heating Process ◽  
Heating And Cooling ◽  
The Magnetic Field

In this paper, we study the self-gravitating accretion disks by considering the toroidal component of magnetic field, [Formula: see text] and wind/outflow in the flow and also investigate the effect of two parameters, [Formula: see text] and [Formula: see text] corresponding to magnetic field on the latitudinal structure of such accretion disks. The cooling of the disk is parameterized simply as, [Formula: see text] (where [Formula: see text] is the internal energy and [Formula: see text] is the cooling timescale and [Formula: see text] is a free constant) and the heating rate is decomposed into two components, magnetic field and viscosity dissipations. We have shown that when the toroidal magnetic field becomes stronger, the heating process (viscous and resistivity) and the radiative cooling rate increase. Ohmic heating is much bigger than viscous heating and cooling, so we must consider the role of the magnetic field in the energy equation. Our numerical solutions show that the thickness of the disk decreases with strong toroidal component of magnetic field. The magnetic field leads to production of the outflow in the low latitude. So, by increasing the toroidal component of the magnetic field, the regions which belong to inflow decrease and the disk is cooled.

Vorticity organization in the outer layer of turbulent channels with disturbed walls

2007 ◽  
Vol 591 ◽  
pp. 145-154 ◽  
Author(s):  
OSCAR FLORES ◽  
JAVIER JIMÉNEZ ◽  
JUAN C. DEL ÁLAMO
Keyword(s):  
Spectral Analysis ◽  
Numerical Experiments ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
The Self ◽  
Average Flow ◽  
Global Modes ◽  
Self Similar ◽  
Using Data

The vortex clusters in the turbulent outer region of rough- and smooth-walled channels, and their associated velocity structures, are compared using data from numerical experiments at friction Reynolds numbers Reτ ≤ 674. The results indicate that the roughness of the wall does not affect their properties, particularly the existence of wall-detached and wall-attached populations, and the self-similar size distribution of the latter. The average flow field conditioned to the attached clusters reveals similar conical structures of low streamwise velocity for the rough- and smooth-walled cases, which eventually grow into the global modes previously identified from spectral analysis. We conclude that the vortex clusters of the turbulent outer region either originate away from the wall, or quickly forget their origin, in agreement with Townsend's similarity hypothesis.

scholarly journals Cylindrically-Collimated, Self-Similar MHD Disk Outflows

1997 ◽  
Vol 163 ◽  
pp. 439-442 ◽  
Author(s):  
Eve C. Ostriker
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Power Law ◽  
Rotating Disks ◽  
Self Similar ◽  
Full Solution ◽  
Flow Variables ◽  
Flow Velocities

AbstractWe describe the dynamics of a class of MHD winds from Keplerian-rotating disks. In this model, all flow velocities are assumed to vary self-similarly with spherical radius r as υ(r, θ) ∝ r−1/2, with density varying as ρ(r, θ) ∝ r−q for arbitrary q. At large distances from the disk, the wind is explicitly required to become cylindrically collimated. We find that the asymptotic wind solution has power-law scalings of all flow variables in the cylindrical radius R = r sin θ, and q < 1 is necessary. We describe how the Alfvén criticality condition limits the space of energy and angular momentum parameters defining these wind solutions. We present an example of the run of density, velocity, and magnetic field for a full solution of the wind equations, and compare the properties of these cylindrically-collimated wind solutions to previous work.

scholarly journals Magnetic Flux Transport in Protostellar Accretion Disks

1997 ◽  
Vol 163 ◽  
pp. 692-692
Author(s):  
John Contopoulos ◽  
Arieh Königl
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Accretion Disks ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Flux Transport ◽  
Disk Structure ◽  
Large Scale Magnetic Field ◽  
Field Lines ◽  
Open Magnetic Field

AbstractCentrifugally driven winds from the surfaces of magnetized accretion disks are a leading candidate for the origin of bipolar outflows and have also been recognized as an attractive mechanism for removing the angular momentum of the accreted matter. The origin of the open magnetic field lines that thread the disk in this scenario is, however, still uncertain. One possibility is that the field lines are transported through the disk, but previous studies have shown that this process is inefficient in disks with turbulent viscosity and diffusivity. Here we examine whether the efficiency can be increased if angular momentum is transported from the disk surfaces by large-scale magnetic fields instead of radially by viscous stresses. In this picture, the removal of angular momentum is associated with the establishment of a global poloidal electric current driven by the radial EMF in the disc, and it does not necessarily need to involve super-Alfvénic outflows. We address this problem in the context of protostellar systems and present representative solutions of the time evolution of a resistive disk that is initially threaded by a uniform vertical field anchored at a large distance from its surfaces. We assume that the angular momentum transport in the disk is controlled by the large-scale magnetic field and take into account the influence of the field on the disk structure.

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