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Research Papers

Characterization of Flow-Magnetic Field Interactions in Magneto-Hydrodynamic Turbulence

[+] Author and Article Information
Jacques C. Richard

Mem. ASME
Senior Lecturer
e-mail: richard@tamu.edu

Gaurav Kumar

Graduate Student
e-mail: gauravkr@neo.tamu.edu
Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843-3141

Tamás Kalmár-Nagy

Mem. ASME
Principal Member Research Staff Mitsubishi Electric Research Laboratory,
Cambridge, MA 02139
e-mail: jcnd@kalmarnagy.com

Sharath S. Girimaji

Mem. ASME
Professor
Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843-3141
e-mail: girimaji@aero.tamu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received January 4, 2012; final manuscript received December 12, 2012; published online January 25, 2013. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 8(3), 031010 (Jan 25, 2013) (12 pages) Paper No: CND-12-1002; doi: 10.1115/1.4023323 History: Received January 04, 2012; Revised December 12, 2012

We examine the complex nonlinear flow-magnetic field dynamics in magneto-hydrodynamic (MHD) turbulence. Using direct numerical simulations (DNS), we investigate the dynamical interactions subject to the influence of a uniform applied background magnetic field. The initial magnetic and kinetic Reynolds numbers (based on Taylor microscale) are 45 and there are no initial magnetic field fluctuations. The sum total of turbulent magnetic and kinetic energies decays monotonically. With time, the turbulent magnetic fluctuations grow by extracting energy from velocity fluctuations. Expectedly, the distribution of energy between kinetic and magnetic fluctuations exhibits large periodic oscillations from the equipartition state due to Alfvén waves. We perform a detailed analysis of the flow-magnetic field coupling and posit a simple model for the energy interchange. Such dynamical analysis can provide the insight required for turbulence control and closure modeling strategies.

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References

Figures

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Fig. 1

Kinetic and Magnetic Energy Decay with eddy turnover time, τ. (B = 0: solid; N = 0.0: _. _. ; N = 0.3: ... ; N = 0.05: - - -) [25].

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Fig. 2

Evolution of EM, EK, Et and Lorentz work with τ. (a) N = 0:3; (b) N = 0:05 (solid: Kinetic Energy; _._. : Total Energy; ... : Lorentz work, - - - : Magnetic Energy) [25].

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Fig. 3

Evolution of helicities with τ (a) N = 0:3; (b) N = 0:05 (solid: Cross Helicity; ... : Kinetic Helicity, - - - : Magnetic Helicity) [25]

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Fig. 4

Evolution of helicities (scaled to kinetic plus magnetic energy) with τ. (a) N = 0:3; (b) N = 0:05 (solid: Cross Helicity; ... : Kinetic Helicity, - - - : Magnetic Helicity) [25]

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Fig. 5

Kinetic and magnetic energy (normalized with total energy) vs. eddy turnover time

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Fig. 9

The Lorentz force at (a) τ = 0:12, (b) τ = 0:18, (c) τ = 0:2 and (d) τ = 0:25

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Fig. 6

Comparison of computational data with proposed model

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Fig. 7

Kinetic and Magnetic Energy plot from the model

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Fig. 8

Evolution of EM/Et and EK/Et with τ. (solid:Kinetic Energy; - - - : Magnetic Energy)

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Fig. 10

Current density progression indicating propagation of Alfvén wavesas also seen in other studies [1] (a) τ = 0:12, (b) τ = 0:138, (c) τ = 0:158, (d) τ = 0:18, (d) τ = 0:2 and (e) τ = 0:25

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Fig. 11

Streamlines at eddy turnover times, (a) τ = 0.18 and (b) τ = 0.25

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Fig. 12

Vorticity field “streamlines” at eddy turnover times, (a) τ = 0.18 and (b) τ = 0.25

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Fig. 13

Magnetic field “streamlines” at eddy turnover times, (a) τ = 0.18 and (b) τ = 0.25

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Fig. 14

Magnitude of the vorticity at (a) τ = 0:12, (b) τ = 0:18, (c) τ = 0:2 and (d) τ = 0:25

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