Abstract
The present work is devoted to study of self-excitation of magnetic field and the motion of the conducting fluid at the same time taking into account acting forces. The idea is to specify in the phase space of initial conditions for the velocity field and magnetic field, which satisfy the condition of continuity. Given initial condition with the phase space is translated into physical space using a Fourier transform. The obtained velocity field and magnetic field are used as initial conditions for the filtered MHD equations. Further is solved the unsteady three-dimensional equation of magnetohydrodynamics to simulate homogeneous MHD turbulence decay.
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References
Batchelor, G.K.: On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. Roy. Soc. A 201(16), 405–416 (1950)
Schumann, U.: Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field. J. Fluid Mech. 74, 31–58 (1976)
Moffatt, H.K.: On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571–592 (1967)
Hossain, M.: Inverse energy cascades in three dimensional turbulence. Phys. Fluids B. 3(2), 511–514 (1991)
Zikanov, O., Thess, A.: Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358(1), 299–333 (1998)
Vorobev, A., Zikanov, O., Davidson, P.A., Knaepen, B.: Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys. Fluid 17 (2005)
Burattini, P., Zikanov, O., Knaepen, B.: Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number. J. Fluid Mech. 657, 502–538 (2010)
Knaepen, B., Kassinos, S., Carati, D.: Magnetohydrodynamic turbulence at moderate magnetic Reynolds number. J. Fluid Mech. 513(3), 199–220 (2004)
Knaepen, B., Moin, P.: Large-eddy simulation of conductive flows at low magnetic Reynolds number. Physics of Fluids 16, 1255–1261 (2004)
Sahoo, G., Perlekar, P., Panditn, R.: Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence. New J. Phys. 13, 1367–2630 (2011)
Ievlev, V.M.: The method of fractional steps for solution of problems of mathematical physics. Science Nauka, Moscow (1975)
Sirovich, L., Smith, L., Yakhot, V.: Energy spectrum of homogeneous and isotropic turbulence in far dissipation range. Physical Review Letters 72(3), 344–347 (1994)
Zhumagulov, B., Abdibekov, U., Zhakebaev, D., Zhubat, K.: Modelling isotropic turbulence decay based on the LES. Mathematical modelling 25(1), 18–32 (2013)
Abdibekov, U.S., Zhakebaev, D.B.: Modelling of the decay of isotropic turbulence by the LES. J. Phys.: Conf. Ser. 318 (2011)
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Abdibekova, A., Zhumagulov, B., Zhakebayev, D. (2015). Modelling of Evolution Small-Scale Magnetohydrodynamic Turbulence Depending on the Magnetic Viscosity of the Environment. In: Danaev, N., Shokin, Y., Darkhan, AZ. (eds) Mathematical Modeling of Technological Processes. CITech 2015. Communications in Computer and Information Science, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-25058-8_2
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DOI: https://doi.org/10.1007/978-3-319-25058-8_2
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