Evolution of Turbulent Magnetic Fields – Approach to a Steady State

1971 ◽  
Vol 43 ◽  
pp. 487-504
Author(s):  
S. Nagarajan
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Dynamical Evolution ◽  
Magnetic Excitation ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Turbulent Dynamo ◽  
Magnetic Spectrum

The dynamical evolution of a weak, random, magnetic excitation in a turbulent electrically-conducting fluid is examined under varying kinematic conditions. It is found that the results of an earlier paper (Kraichnan and Nagarajan, 1967) can be reliably extended to a stage of evolution wherein the magnetic spectrum has reached local equipartition with the velocity. The transfer of the magnetic energy to smaller wavenumbers (larger scales) is considerable and significant. This result is highly pertinent to the turbulent dynamo question, which has been variously investigated recently. The relevance of the coupling of the rms magnetic field to the magnetic modes of all scales in deciding the efficiency of this transfer is discussed.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

scholarly journals Turbulent dynamo in a collisionless plasma

2016 ◽  
Vol 113 (15) ◽  
pp. 3950-3953 ◽  
Author(s):  
François Rincon ◽  
Francesco Califano ◽  
Alexander A. Schekochihin ◽  
Francesco Valentini
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Collisionless Plasma ◽  
High Energy ◽  
Nearby Galaxy ◽  
Astrophysical Plasmas ◽  
Flow Energy ◽  
Field Amplification ◽  
Turbulent Dynamo

Magnetic fields pervade the entire universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times (up to microgauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions, and on scales of at least tens of kiloparsecs) are major puzzles largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context; however, extragalactic plasmas are weakly collisional (as opposed to magnetohydrodynamic fluids), and whether magnetic field growth and sustainment through an efficient turbulent dynamo instability are possible in such plasmas is not established. Fully kinetic numerical simulations of the Vlasov equation in a 6D-phase space necessary to answer this question have, until recently, remained beyond computational capabilities. Here, we show by means of such simulations that magnetic field amplification by dynamo instability does occur in a stochastically driven, nonrelativistic subsonic flow of initially unmagnetized collisionless plasma. We also find that the dynamo self-accelerates and becomes entangled with kinetic instabilities as magnetization increases. The results suggest that such a plasma dynamo may be realizable in laboratory experiments, support the idea that intracluster medium turbulence may have significantly contributed to the amplification of cluster magnetic fields up to near-equipartition levels on a timescale shorter than the Hubble time, and emphasize the crucial role of multiscale kinetic physics in high-energy astrophysical plasmas.

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Average Nusselt Number ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Square Cavity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Double Diffusive

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

scholarly journals Generalized function treatment of the Alfvén-gravity wave problem

1983 ◽  
Vol 6 (2) ◽  
pp. 395-402
Author(s):  
L. Debnath ◽  
K. Vajravelu
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Function Method ◽  
Radiation Condition ◽  
Physical Significance ◽  
Generalized Function ◽  
Wave Problem ◽  
Physical Interest ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.

scholarly journals Magnetic Braking and the Oblique Rotator Model

1970 ◽  
Vol 4 ◽  
pp. 269-273
Author(s):  
L. Mestel ◽  
C. S. Selley
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Stellar Wind ◽  
Rotation Axis ◽  
Dynamical Evolution ◽  
Magnetic Star ◽  
Rotator Model ◽  
Oblique Rotator ◽  
Magnetic Braking

This work investigates the dynamical evolution of a rotating magnetic star which drives a stellar wind. The basic magnetic field of the star is supposed symmetric about an axis, which is inclined at an angle X to the rotation axis k (Figure 1). We adopt the familiar equations of an inviscid perfectly conducting gas. In a steady state, the velocity as seen in a frame rotating with the star is taken as

Boundary layers of an anchored magnetic field in a highly conductive flow

2010 ◽  
Vol 466 (2123) ◽  
pp. 3153-3166 ◽  
Author(s):  
Manuel Núñez ◽  
Alberto Lastra
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Order Approximation ◽  
First Order ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
First Order Approximation ◽  
Distance To The Boundary

The effects of the flow of an electrically conducting fluid upon a magnetic field anchored at the boundary of a domain are studied. By taking the resistivity as a small parameter, the first-order approximation of an asymptotic analysis yields a boundary layer for the magnetic potential. This layer is analysed both in general and in three particular cases, showing that while in general its effects decrease exponentially with the distance to the boundary, several additional effects are highly relevant.

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