scholarly journals The self-similar structure of advection-dominated discs with outflow and radial viscosity

2020 ◽  
Vol 493 (4) ◽  
pp. 5107-5119
Author(s):  
S M Ghoreyshi ◽  
M Shadmehri
Keyword(s):  
Magnetic Field ◽  
Similarity Solutions ◽  
Observational Evidence ◽  
The Self ◽  
Accretion Discs ◽  
Gas Velocity ◽  
State Structure ◽  
Self Similar ◽  
Strong Winds ◽  
The Magnetic Field

ABSTRACT Observational evidence and theoretical arguments postulate that outflows may play a significant role in the advection-dominated accretion discs (ADAFs). While the azimuthal viscosity is the main focus of most previous studies in this context, recent studies indicated that disc structure can also be affected by the radial viscosity. In this work, we incorporate these physical ingredients and the toroidal component of the magnetic field to explore their roles in the steady-state structure of ADAFs. We thereby present a set of similarity solutions where outflows contribute to the mass loss, angular momentum removal, and the energy extraction. Our solutions indicate that the radial viscosity causes the disc to rotate with a slower rate, whereas the radial gas velocity increases. For strong winds, the infall velocity may be of order the Keplerian speed if the radial viscosity is considered and the saturated conduction parameter is high enough. We show that the strength of magnetic field and of wind can affect the effectiveness of radial viscosity.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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 Study on Fluidization Characteristics of Magnetically Fluidized Beds for Microfine Particles

Minerals ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 61
Author(s):  
Yakun Tian ◽  
Shulei Song ◽  
Xuan Xu ◽  
Xinyu Wei ◽  
Shanwen Yan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Fluidized Bed ◽  
Magnetic Field Strength ◽  
Fluidized Beds ◽  
Expansion Rate ◽  
Gas Velocity ◽  
Bed Height ◽  
Bed Expansion ◽  
The Magnetic Field

The bed pressure drop, minimum fluidized gas velocity, bed density, and bed expansion rate are important parameters characterizing the fluidization characteristics of gas-solid fluidized beds. By analyzing these parameters, the advantages and disadvantages of the fluidization state can be known. In this study, experiments were conducted to study the fluidization characteristics of a gas-solid magnetically fluidized bed for microfine particles by changing the magnetic field strength, magnetic field addition sequence, and static bed height. The experimental results show that when the magnetic field strength increased from 0 KA/m to 5 KA/m, the minimum fluidized gas velocity of particles increased from 4.42 cm/s to 10.32 cm/s, while the bed pressure drop first increased and then decreased. When the magnetic field strength is less than 3.4 KA/m, the microfine particles in the bed are mainly acted on by the airflow; while when the magnetic field strength is greater than 3.4 KA/m, the microfine particles are mainly dominated by the magnetic field. The magnetic field addition sequence affects the fluidization quality of microfine particles. The fluidized bed with ‘adding magnetic field first’ shows a more stable fluidization state than ‘adding magnetic field later’. Increasing of the static bed height reduces the bed expansion rate. The bed expansion rate is up to 112.5% at a static bed height of h0 = 40 mm and H = 5 KA/m. This will broaden the range of density regulation of a single magnetic particle and lay the advantage of gas-solid magnetically fluidized bed for microfine particles in the field of separation of fine coal.

scholarly journals Mathematical Theory of Cylindrical Isothermal Blast Waves in a Magnetic Field

1981 ◽  
Vol 34 (3) ◽  
pp. 279 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Supernova Remnants ◽  
Magnetic Pressure ◽  
Blast Waves ◽  
Physical Domain ◽  
Fluid Flow Velocity ◽  
Magnetic Tension ◽  
Self Similar ◽  
The Magnetic Field ◽  
Similar Flows

An investigation is made of the self-similar flow behind a cylindrical blast wave from a line explosion (situated on r = 0, using conventional cylindrical coordinates r, 4>, z) in a medium whose density and magnetic field both vary as r -w ahead of the blast front, with the assumption that the flow is isothermal. The magnetic field can have components in both the azimuthal B(jJ and longitudinal B, directions. It is found that: (i) For B(jJ =f:. 0 =f:. B, a continuous single-valued solution with a velocity field representing outflow of material away from the line of explosion does not exist for OJ OJ > 0 the governing equation possesses a set of movable critical points. In this case it is shown that the fluid flow velocity is bracketed between two curves and that the asymptotes of the velocity curve on the shock are intersected by, or are tangent to, the two curves. Thus a solution always exists in the physical domain r ~ o. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results have an impact upon previous applications of the theory of self-similar flows to evolving supernova remnants without allowance for the dynamical influence of magnetic pressure and magnetic tension.

scholarly journals Warped Accretion Discs

2003 ◽  
Vol 208 ◽  
pp. 385-386
Author(s):  
D. Chakrabarty ◽  
J. Murray ◽  
G.A. Wynn ◽  
A.R. King
Keyword(s):  
Magnetic Field ◽  
Modal Analysis ◽  
Numerical Investigation ◽  
Fourier Transforms ◽  
Small Difference ◽  
Accretion Discs ◽  
Stellar Systems ◽  
Hydrodynamic Simulations ◽  
Companion Star ◽  
The Magnetic Field

In this article we report the results of our numerical investigation of warped accretion discs in binary stellar systems. We perform complete 3-D hydrodynamic simulations of binary discs. The disc is rendered unstable to the warp mode under the action of the magnetic field of the companion star in the binary. The disc thus warped is noted to undergo retrograde precession with a precession period just slightly less than the binary period. This small difference in periods can explain the phenomenon of negative superhumps observed in a number of binaries. Besides the modal analysis based on Fourier transforms, warps were also studied by a simple and robust technique that we developed; this is based on an analysis of the azimuthal distributions of particles that lie above and below the mid-plane of the disc.

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.

The self-similar, non-linear evolution of rotating magnetic flux ropes

1995 ◽  
Vol 13 (8) ◽  
pp. 815-827 ◽  
Author(s):  
C. J. Farrugia ◽  
V. A Osherovich ◽  
L. F. Burlaga
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Small Amplitude ◽  
Symmetry Axis ◽  
Flux Rope ◽  
Magnetic Clouds ◽  
Linear Evolution ◽  
Multiplicative Factor ◽  
Self Similar ◽  
The Magnetic Field

Abstract. We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the "separable" class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity Ωcrit, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation ω is inversely proportional to the angular velocity of rotation Ω; the product ωΩbeing proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that at 1 AU only a minority do. We discuss data on two magnetic clouds where we interpret the presence in each of vortical plasma motion about the symmetry axis as a sign of rotation. Our estimates for the angular velocities suggest that the parameters of the two magnetic clouds are below critical values. The two clouds differ in many respects (such as age, bulk flow speed, size, handedness of the magnetic field, etc.), and we find that their rotational parameters reflect some of these differences, particularly the difference in age. In both clouds, a rough estimate of the radial electric field in the rigidly rotating core, calculated in a non-rotating frame, yields values of the order mV m–1.

scholarly journals No-z model: results and perspectives for accretion discs

2021 ◽  
pp. 490-494
Author(s):  
E. A. Mikhailov ◽  
M. V. Pashentsevay
Keyword(s):  
Magnetic Field ◽  
Black Holes ◽  
Magnetic Fields ◽  
Variable Stars ◽  
Field Structure ◽  
Accretion Discs ◽  
Astrophysical Objects ◽  
The Galaxy ◽  
Galaxy Center ◽  
The Magnetic Field

Accretion discs surround different compact astrophysical objects such as black holes, neutron stars and white dwarfs. Also they are situated in systems of variable stars and near the galaxy center. Magnetic fields play an important role in evolution and hydrodynamics of the accretion discs: for example, they can describe such processes as the transition of the angular momentum. There are different approaches to explain the magnetic fields, but most interesting of them are connected with dynamo generation. As for disc, it is quite useful to take no-$z$ approximation which has been developed for galactic discs to solve the dynamo equations. It takes into account that the disc is quite thin, and we can solve the equations only for two plane components of the field. Here we describe the time dependence of the magnetic field for different distances from the center of the disc. Also we compare the results with another approaches which take into account more complicated field structure.

scholarly journals Ellipsoids (v1.0): 3D Magnetic modelling of ellipsoidal bodies

2017 ◽  
Author(s):  
Diego Takahashi Tomazella ◽  
Vanderlei C. Oliveira Jr.
Keyword(s):  
Magnetic Field ◽  
Synthetic Data ◽  
The Self ◽  
Geological Body ◽  
Python Language ◽  
Wide Range ◽  
Magnetic Modelling ◽  
And Inversion ◽  
The Magnetic Field ◽  
Limiting Value

Abstract. A considerable amount of literature has been published on the magnetic modelling of uniformly magnetized ellipsoids since the second half of the nineteenth century. Ellipsoids have flexibility to represent a wide range of geometrical forms, are the only known bodies which can be uniformly magnetized in the presence of a uniform inducing field and are the only bodies for which the self-demagnetization can be treated analytically. This property makes ellipsoids particularly useful for modelling compact orebodies having high susceptibility. In this case, neglecting the self-demagnetization may strongly mislead the interpretation of these bodies by using magnetic methods. A number of previous studies consider that the self-demagnetization can be neglected for the case in which the geological body has an isotropic susceptibility lower than or equal to 0.1 SI. This limiting value, however, seems to be determined empirically and there has been no discussion about how this value was determined. Besides, the geoscientific community lacks an easy-to-use tool to simulate the magnetic field produced by uniformly magnetized ellipsoids. Here, we present an integrated review of the magnetic modelling of arbitrarily oriented triaxial, prolate and oblate ellipsoids. Our review includes ellipsoids with both induced and remanent magnetization, as well as with isotropic or anisotropic susceptibility. We also propose a way of determining the isotropic susceptibility above which the self-demagnetization must be taken into consideration. Tests with synthetic data validate our approach. Finally, we provide a set of routines to model the magnetic field produced by ellipsoids. The routines are written in Python language as part of the Fatiando a Terra, which is an open-source library for modelling and inversion in geophysics.

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