Inverse cascades in incompressible fluid and magnetofluid turbulence

1996 ◽  
Vol 56 (3) ◽  
pp. 467-491
Author(s):  
Murshed Hossain
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Uniform Magnetic Field ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Self Organization ◽  
Anisotropic Fluid ◽  
Uniform Rotation ◽  
Fluid Turbulence ◽  
Turbulent Fluctuations

Absolute equilibrium statistical theory and numerical simulations are reviewed in the context of inverse cascades in two- and three-dimensional incompressible fluid and magnetofluid turbulence. Turbulent fluctuations of physically interesting quantities undergo inverse cascade to larger spatial scales, leading to self-organization under certain circumstances. In particular, most systems with more than one quadratic ideal invariant, or, having some kind of imposed anisotropy, exhibit inverse cascades. Anisotropic fluid turbulence in the presence of a uniform rotation and magnetofluid turbulence in the presence of a uniform magnetic field are considered.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

Liquid-metal flow in a system of electrically coupled U-bends in a strong uniform magnetic field

1995 ◽  
Vol 299 ◽  
pp. 73-95 ◽  
Author(s):  
Sergei Molokov ◽  
Robert Stieglitz
Keyword(s):  
Magnetic Field ◽  
Pressure Drop ◽  
Liquid Metal ◽  
Uniform Magnetic Field ◽  
Flow Direction ◽  
Metal Flow ◽  
Three Dimensional ◽  
Recirculatory Flow ◽  
The Magnetic Field ◽  
Very High

Liquid-metal magnetohydrodynamic flow in a system of electrically coupled U-bends in a strong uniform magnetic field is studied. The ducts composing the bends are electrically conducting and have rectangular cross-sections. It has been anticipated that very strong global electric currents are induced in the system, which modify the flow pattern and produce a very high pressure drop compared to the flow in a single U-bend. A detailed asymptotic analysis of flow for high values of the Harmann number (in fusion blanket applications of the order of 103−104) shows that circulation of global currents results in several types of peculiar flow patterns. In ducts parallel to the magnetic field a combination of helical and recirculatory flow types may be present and vary from one bend to another. The magnitude of the recirculatory motion may become very high depending on the flow-rate distribution between the bends in the system. The recirculatory flow may account for about 50% of the flow in all bends. In addition there are equal and opposite jets at the walls parallel to the magnetic field, which are common to any two bends. The pressure drop due to three-dimensional effects linearly increases with the number of bends in a system and may significantly affect the total pressure drop. To suppress this and some other unwelcome tendencies either the ducts perpendicular to the magnetic field should be electrically separated, or the flow direction in the neighbouring ducts should be made opposite, so that leakage currents cancel each other.

Weak magnetohydrodynamic turbulence and intermittency

2015 ◽  
Vol 770 ◽  
Author(s):  
R. Meyrand ◽  
K. H. Kiyani ◽  
S. Galtier
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Three Dimensional ◽  
Leading Order ◽  
Magnetohydrodynamic Turbulence ◽  
Asymptotic Regime ◽  
Resonant Interactions ◽  
Vector Separation ◽  
Parallel Current

Three-dimensional numerical simulation is used to investigate intermittency in incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field $\boldsymbol{b}_{\mathbf{0}}$ and zero cross-helicity. At leading order, this asymptotic regime is achieved via three-wave resonant interactions with the scattering of a wave on a 2D mode for which $k_{\Vert }=0$. When the interactions with the 2D modes are artificially reduced, we show numerically that the system exhibits an energy spectrum with $k_{\bot }^{-3/2}$, whereas the expected exact solution with $k_{\bot }^{-2}$ is recovered with the full nonlinear system. In the latter case, strong intermittency is found when the vector separation of structure functions is taken transverse to $\boldsymbol{b}_{\mathbf{0}}$. This result may be explained by the influence of the 2D modes whose regime belongs to strong turbulence. In addition to shedding light on the origin of this intermittency, we derive a log-Poisson law, ${\it\zeta}_{p}=p/8+1-(1/4)^{p/2}$, which fits the data perfectly and highlights the important role of parallel current sheets.

scholarly journals Dynamo action in the presence of an imposed magnetic field

2009 ◽  
Vol 465 (2105) ◽  
pp. 1599-1616 ◽  
Author(s):  
D.W. Hughes ◽  
M.R.E. Proctor
Keyword(s):  
Magnetic Field ◽  
Linear Stability ◽  
Uniform Magnetic Field ◽  
Three Dimensional ◽  
Background Field ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Circularly Polarized ◽  
Forcing Function ◽  
Basic States

We consider the linear stability to three-dimensional perturbations of two-dimensional nonlinear magnetohydrodynamic basic states obtained from a specified forcing function in the presence of an imposed initially uniform magnetic field of strength B 0 . The forcing is chosen such that it drives the ‘circularly polarized’ (CP) flow of Galloway & Proctor ( Galloway & Proctor 1992 Nature 356 , 691–693) when B 0 =0. We first examine the properties of these basic states and their dependence on B 0 and the magnetic Reynolds number Rm . The linear stability of these states is then investigated. It is found that, at a given Rm , the presence of a background field is stabilizing. The results also allow us to speculate that, at a fixed value of B 0 , the growth of the unstable perturbations is ‘fast’, in the sense that the growth rate becomes independent of Rm as Rm →∞.

scholarly journals Convective mechanism of amplification and structuring of magnetic fields

2012 ◽  
Vol 8 (S294) ◽  
pp. 137-142
Author(s):  
A. V. Getling ◽  
V. V. Kolmychkov ◽  
O. S. Mazhorova
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Incompressible Fluid ◽  
Spatial Scales ◽  
Fluid Motion ◽  
Horizontal Layer ◽  
Field Lines ◽  
The Magnetic Field ◽  
Initial Magnetic Field ◽  
Peripheral Regions

AbstractMagnetoconvection in a horizontal layer of incompressible fluid is simulated numerically. The initial magnetic field is assumed to be uniform and horizontal. The interaction of quasi-ordered cellular convection with the magnetic field is shown to be able to produce bipolar (and also diverse more complex) configurations of a substantially amplified magnetic field. The operation of this mechanism, which can be regarded as a modification of the mechanism suggested by Tverskoi (1966), is controlled by the very topology of the cellular flow, should be manifest on various spatial scales, and does not require strong initial fields. Magnetic configurations develop both in the central parts of convection cells, where circulatory fluid motion “winds” magnetic field lines, and in the network formed by their peripheral regions due to the “sweeping” of magnetic field lines.

scholarly journals Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field

1976 ◽  
Vol 74 (1) ◽  
pp. 31-58 ◽  
Author(s):  
U. Schumann
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Energy Transfer ◽  
Incompressible Fluid ◽  
Uniform Magnetic Field ◽  
Two Dimensional ◽  
Static Approximation ◽  
Return To Equilibrium ◽  
The Magnetic Field ◽  
High Wavenumbers

The transition of homogeneous turbulence from an initially isotropic three-dimensional to a quasi-two-dimensional state is simulated numerically for a conducting, incompressible fluid under a uniform magnetic fieldB0. The magnetic Reynolds number is assumed to be small, so that the induced fluctuations of the magnetic field are small compared with the imposed magnetic fieldB0, and can be computed from a quasi-static approximation. If the imposed magnetic field is strong enough, all variations of the flow field in the direction ofB0are damped out. This effect is important e.g. in the design of liquid-metal cooling systems for fusion reactors, and the properties of the final state are relevant to atmospheric turbulence. An extended version of the code of Orszag & Patterson (1972) is used to integrate the Navier-Stokes equations for an incompressible fluid. The initial hydrodynamic Reynolds number is 60. The magnetic interaction numberNis varied between zero and 50. Periodic boundary conditions are used. The resolution corresponds to 323points in real space. The full nonlinear simulations are compared with otherwise identical linear simulations; the linear results agree with the nonlinear ones within 3% for about one-fifth of the large-scale turnover time. This departure is a consequence of the return-to-equilibrium tendencies caused mainly by energy transfer towards high wavenumbers. The angular energy transfer and the energy exchange between different components are smaller, and become virtually zero for large values ofN. ForN≈ 50 we reach a quasi-two-dimensional state. Here, the energy transfer towards high wavenumbers is reduced for the velocity components perpendicular toB0but relatively increased for the component parallel toB0. The overall behaviour is more similar to three-than to purely two-dimensional turbulence. This finding is of great importance for turbulence models of the atmosphere. The realization of a purely two-dimensional state does not seem to be possible for decaying turbulence. The magnetic field causes highly intensified pressure fluctuations, which contribute to the redistribution of the anisotropic Lorentz forcing.

scholarly journals FERMI SURFACES OF CRYSTALS IN A HIGH MAGNETIC FIELD

2003 ◽  
Vol 02 (06) ◽  
pp. 603-610 ◽  
Author(s):  
J. BRÜNING ◽  
V. V. DEMIDOV ◽  
V. A. GEYLER
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Dispersion Relation ◽  
Potential Theory ◽  
Explicit Form ◽  
High Magnetic Field ◽  
Uniform Magnetic Field ◽  
Three Dimensional ◽  
Fermi Surfaces ◽  
Zero Range

A method of building and investigation of the Fermi surfaces for three-dimensional crystals subjected to a uniform magnetic field is presented. The Hamiltonian of a charged particle in the crystal is treated in the framework of the zero-range potential theory. The dispersion relation for the Hamiltonian is obtained in an explicit form.

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