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Research Papers: Fundamental Issues and Canonical Flows

Magnetohydrodynamic Turbulence Decay Under the Influence of Uniform or Random Magnetic Fields

[+] Author and Article Information
Jacques C. Richard1

 Department of Aerospace Engineering, Texas A & M University, College Station, TX, 77843-3141richard@tamu.edu

Benjamin M. Riley

 Department of Aerospace Engineering, Texas A & M University, College Station, TX, 77843-3141

Sharath S. Girimaji

 Department of Aerospace Engineering, Texas A & M University, College Station, TX, 77843-3141girimaji@aero.tamu.edu

1

Corresponding author.

J. Fluids Eng 133(8), 081205 (Sep 02, 2011) (10 pages) doi:10.1115/1.4003985 History: Received September 21, 2010; Revised April 07, 2011; Published September 02, 2011; Online September 02, 2011

We perform direct numerical simulations of decaying magnetohydrodynamic turbulence subject to initially uniform or random magnetic fields. We investigate the following features: (i) kinetic–magnetic energy exchange and velocity field anisotropy, (ii) action of Lorentz force, (iii) enstrophy and helicity behavior, and (iv) internal structure of the small scales. While tendency toward kinetic–magnetic energy equi-partition is observed in both uniform and random magnetic field simulations, the manner of approach to that state is very different in the two cases. Overall, the role of the Lorentz force is merely to bring about the equi-partition. No significant variance anisotropy of velocity fluctuations is observed in any of the simulations. The mechanism of enstrophy generation changes with the strength of the magnetic field, and helicity shows no significant growth in any of the cases. The small-scale structure (orientation between vorticity and strain-rate eigenvectors) does not appear to be influenced by the magnetic field.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kinetic and magnetic energy and enstrophy decay with eddy turnover time, τ. (Case I: B=0, solid line; Case IIa: N=0.0, dash-dotted line; Case III: N=0.3, dotted line; Case IV: N = 05: dashed line.)

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Figure 2

(a) Evolution of Ek and the square of its individual contributing velocity components with τ for N=0 and (b) N=0.05, (c) N=0.3, averaged over the flow domain; and (d) evolution of the square of the individual contributing magnetic field components, as indicator of anisotropy, normalized to B'2 then averaged over the flow domain, for N=0.3

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Figure 3

Evolution of Em, Ek, Etotal and Lorentz energy with τ. (Solid line: kinetic energy; dash-dotted line: total energy; dotted line: Lorentz energy; dashed line: magnetic energy.)

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Figure 4

PDF of the time rate of change of enstrophy at τ=0.25 (solid line: B=0; dotted line: N=0.05; dash-dotted line: N=0.3, dashed line: N=0)

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Figure 5

PDF of the different components of the total time rate of change of enstrophy at τ=0.25

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Figure 6

Evolution of helicities with τ (solid line: cross-helicity; dotted line: kinetic helicity, dashed line: magnetic helicity)

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Figure 7

Evolution of helicities (scaled to kinetic plus magnetic energy) with τ (solid line: cross-helicity; dotted line: kinetic helicity, dashed line: magnetic helicity)

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Figure 8

PDF of the eigenvalues of the velocity strain rate tensor at τ=0.25 versus [α,β,γ]/α2+β2+γ2

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Figure 9

PDF of the vorticity alignment to the eigenvalues of the velocity strain rate tensor at τ=0.25: solid line: ω→×λ→α/ω2λα2; dashed line: ω→×λ→β/ω2λβ2; dash-dotted line: ω→×λ→γ/ω2λγ2

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