scholarly journals Lack of universality in MHD turbulence, and the possible emergence of a new paradigm?

2010 ◽  
Vol 6 (S271) ◽  
pp. 304-316 ◽  
Author(s):  
Annick Pouquet ◽  
Marc-Etienne Brachet ◽  
Ed Lee ◽  
Pablo Mininni ◽  
Duane Rosenberg ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Magnetic Helicity ◽  
Alfvén Waves ◽  
Focus Attention ◽  
New Paradigm ◽  
Mhd Turbulence ◽  
Magnetic Prandtl Number ◽  
Astrophysical Objects

AbstractWe review some of the recent results obtained in MHD turbulence, as encountered in many astrophysical objects. We focus attention on the lack of universality in such flows, including in the simplest case (no externally imposed magnetic field, no forcing, unit magnetic Prandtl number). Several parameters can foster such a breakdown of classical Kolmogorov scaling, such as the presence of velocity-magnetic field correlations, or of magnetic helicity and the role of the interplay between nonlinear eddies and Alfvén waves. A link with avalanche processes is also discussed. These findings have led to the conjecture of the emergence of a new paradigm for MHD turbulence, as a possibly unsettled competition between several dynamical phenomena.

scholarly journals Two-dimensional magnetohydrodynamic turbulence in the small magnetic Prandtl number limit

2012 ◽  
Vol 703 ◽  
pp. 85-98 ◽  
Author(s):  
David G. Dritschel ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Spectral Method ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetic Prandtl Number ◽  
Wide Range ◽  
Lagrangian Advection ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

AbstractIn this paper we introduce a new method for computations of two-dimensional magnetohydrodynamic (MHD) turbulence at low magnetic Prandtl number $\mathit{Pm}= \nu / \eta $. When $\mathit{Pm}\ll 1$, the magnetic field dissipates at a scale much larger than the velocity field. The method we utilize is a novel hybrid contour–spectral method, the ‘combined Lagrangian advection method’, formally to integrate the equations with zero viscous dissipation. The method is compared with a standard pseudo-spectral method for decreasing $\mathit{Pm}$ for the problem of decaying two-dimensional MHD turbulence. The method is shown to agree well for a wide range of imposed magnetic field strengths. Examples of problems for which such a method may prove invaluable are also given.

scholarly journals Magnetic Field Confinement in the Corona: The Role of Magnetic Helicity Accumulation

2006 ◽  
Vol 644 (1) ◽  
pp. 575-586 ◽  
Author(s):  
Mei Zhang ◽  
Natasha Flyer ◽  
Boon Chye Low
Keyword(s):  
Magnetic Field ◽  
Magnetic Helicity

Compositional convection in the presence of a magnetic field. II. Cartesian plume

2005 ◽  
Vol 461 (2060) ◽  
pp. 2605-2633 ◽  
Author(s):  
I.A Eltayeb ◽  
E.A Hamza ◽  
J.A Jervase ◽  
E.V Krishnan ◽  
D.E Loper
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Single Interface ◽  
Magnetic Prandtl Number ◽  
Infinite Extent ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Field Inclination

The analysis of part I, dealing with the morphological instability of a single interface in a fluid of infinite extent, is extended to the case of a Cartesian plume of compositionally buoyant fluid, of thickness 2 x 0 , enclosed between two vertical interfaces. The problem depends on six dimensionless parameters: the Prandtl number, σ ; the magnetic Prandtl number, σ m ; the Chandrasekhar number, Q c ; the Reynolds number, Re ; the ratio, B v , of vertical to horizontal components of the ambient magnetic field and the dimensionless plume thickness. Attention is focused on the preferred mode of instability, which occurs in the limit Re ≪1 for all values of the parameters. This mode can be either sinuous or varicose with the wavenumber vector either vertical or oblique , comprising four types. The regions of preference of these four modes are represented in regime diagrams in the ( x 0 ,  σ ) plane for different values of σ m , Q c , B v . These regions are strongly dependent on the field inclination and field strength and, to a lesser extent, on magnetic diffusion. The overall maximum growth rate for any prescribed set of the parameters σ m , Q c , B v , occurs when 1.3< x 0 <1.7, and is sinuous for small σ and varicose for large σ . The magnetic field can enhance instability for a certain range of thickness of the plume. The enhancement of instability is due to the interaction of the field with viscous diffusion resulting in a reverse role for viscosity. The dependence of the helicity and α -effect on the parameters is also discussed.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

scholarly journals MAGNETOHYDRODYNAMIC HEAT AND MASS TRANSFER FLOW WITH INDUCED MAGNETIC FIELD AND VISCOUS DISSIPATIVE EFFECTS

2014 ◽  
Vol 44 (1) ◽  
pp. 9-17
Author(s):  
S. AHMED ◽  
A. BATIN
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Current Density ◽  
Schmidt Number ◽  
Porous Plate ◽  
Mhd Flow ◽  
Induced Magnetic Field ◽  
Dissipative Effects ◽  
Magnetic Prandtl Number ◽  
Mhd Propulsion

An approximate solution to the problem of steady free convective MHD flow of an incompressible viscous electrically-conducting fluid over an infinite vertical isothermal porous plate with mass convection is presented here. A uniform magnetic field is assumed to be applied transversely to the direction of the flow, taking into account the induced magnetic field with viscous and magnetic dissipations of energy. The dimensionless governing equations are solved by using the series solution method. The induced magnetic field, current density, temperature gradient and flow velocity are studied for magnetohydrodynamic body force, magnetic Prandtl number, Schmidt number and Eckert number. It is observed that the induced magnetic field is found to increase with a rise in magnetic Prandtl number. Current density is strongly reduced with increasing magnetic Prandtl number, but enhanced with Schmidt number. The acquired knowledge in our study can be used by designers to control MHD flow as suitable for a certain applications such as laminar magneto-aerodynamics, and MHD propulsion thermo-fluid dynamics.

scholarly journals The convective instability of a Maxwell–Cattaneo fluid in the presence of a vertical magnetic field

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200494
Author(s):  
I. A. Eltayeb ◽  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Critical Rayleigh Number ◽  
Free Boundaries ◽  
Governing Equations ◽  
Horizontal Scale ◽  
Temperature Relation ◽  
Magnetic Prandtl Number ◽  
Zero Values ◽  
Chandrasekhar Number

We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell–Cattaneo (MC) heat flux–temperature relation. We extend the work of Bissell ( Proc. R. Soc. A 472, 20160649 (doi:10.1098/rspa.2016.0649)) to non-zero values of the magnetic Prandtl number p m . With non-zero p m , the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number Q confirms that the MC effect becomes important when C Q 1/2 is O (1), where C is the MC number. In this regime, we derive a scaled system that is independent of Q . When CQ 1/2 is large, the results are consistent with those derived from the governing equations in the limit of Prandtl number p  → ∞ with p m finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large p m regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For Q  ≫ 1 and small values of p , we show that the critical Rayleigh number is non-monotonic in p provided that C  > 1/6. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading-order results.

scholarly journals Generation and propagation of Alfvén waves in solar atmosphere

2008 ◽  
Vol 4 (S257) ◽  
pp. 555-561 ◽  
Author(s):  
Yuri T. Tsap ◽  
Alexander V. Stepanov ◽  
Yulia. G. Kopylova
Keyword(s):  
Magnetic Field ◽  
Cutoff Frequency ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Flux Tubes ◽  
Convective Motions ◽  
Magnetic Flux Tubes ◽  
The Magnetic Field ◽  
Lower Chromosphere

AbstractThe propagation of Alfvén waves from the photosphere into the corona with regard to the fine structure of the magnetic field is considered. The energy flux of Alfvén–type waves generated in the photosphere by convective motions does not depend on the ionization ratio. The reflection coefficient continuously decreases with a decrease of wave period. Influence of the external magnetic field on the Spruit cutoff frequency for transverse (kink) modes excited in the thin magnetic flux tubes is analyzed. Torsional modes can penetrate into the upper atmosphere most effectively since their amplitudes does not increase with height in the photosphere while kink ones can be transformed into shock waves in the lower chromosphere because of a significant increase of amplitudes. In spite of stratification the linearity of Alfvén–type modes in the chromosphere is conserved due to violation of the WKB approximation. The important role of the magnetic canopy is discussed. Alfvén waves generated by convective motions in the photosphere can contribute significantly to the heating of the coronal plasma in quite regions of the Sun.

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