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Compressible Turbulence

Magnetic Reynolds Number Effects on MHD Turbulence
Ladeinde, F. and Gaitonde, D.V., Physics of Fluids 16 (6), pp. 1997-2021 (2004);
https://doi.org/10.1063/1.1736674

Abstract
The effects of the magnetic Reynolds number, Re๐œŽ, on decaying two-dimensional compressible magnetohydrodynamic (MHD) turbulence are investigated through direct numerical simulations. The initial relative intensities of, and the correlation between, the fluctuating velocity (u) and magnetic induction (b) fields are also varied, as measured with the respective parameters f and angle ฮธ. The investigations cover the parameter ranges 1โฉฝRe๐œŽโฉฝ250, 0ยฐโฉฝฮธโฉฝ90ยฐ, and 1โฉฝfโฉฝ3. The results suggest that, at the lowest Re๐œŽReฯƒ investigated, the magnetic field has a negligible impact on the evolution of the turbulence kinetic energy ๐ธ๐‘˜. At higher Re๐œŽ values, when magnetic effects are important, the magnetic field tends to accelerate the decay of the turbulence energy relative to non-MHD flows. On the other hand, the magnetic energy ๐ธ๐‘ shows the opposite trend, being rapidly driven from its initial values to essentially zero very early in the transient at lower Re๐œŽ values, while higher Re๐œŽ values significantly retard this decay. An enhancement of density fluctuations is noted in the intermediate Re๐œŽ range. An interesting observation pertaining to the normalized cross helicity is the fast decay to zero of this quantity when Re๐œŽ=1, independent of the values of ฮธ and f. That is, the fluctuating u and b fields tend to be uncorrelated when the magnetic Reynolds number is low. In this case, the role of the magnetic field is passive, and it is merely convected by the velocity field. The conditions required to maintain a high correlation during the evolution are discussed. We have also seen that the ๐ธ๐‘ decay mode is less sensitive to the value of ฮธ than that of ๐ธ๐‘˜. The relative contribution of ๐ธ๐‘˜,๐ธ๐‘, and the internal energy ๐ธ๐‘– to the total energy ๐ธ๐‘ก is discussed in relation to the values of f, ฮธ, and Re๐œŽ.

Related Papers

  • Ladeinde, F. & Gaitonde, D.V. 2004. Magnetic Reynolds Number Effects on MHD Turbulence. Physics of Fluids Vol. 16  (6), pp. 1997-2021, https://doi.org/10.1063/1.1736674 (2004)
  • Ladeinde, F. & Wu, J. 2002. Second Order Nonlinear Spatial Stability of Compressible Mixing Layers. Physics of Fluids, Vol. 14 (9), pp. 2968-2986, https://doi10.1063/1.1492284  (2001)
  • Cai, X., O'Brien, E. E. & Ladeinde, F. 1998. Advection of Mass Fraction in Forced, Homogeneous, Compressible Turbulence. Physics of Fluids, Vol. 10 (9), pp. 2249-2259, https://doi.org/10.1063/1.869746, (1998)
  • Ladeinde, F. Liu, W., & O'Brien, E. E., โ€œTurbulence in Compressible Mixing Layers. ASME Journal of Fluids Engineering,โ€ Vol. 120, No. 1, 1998, pp. 48-53 https://doi:10.1115/1.2819659  (1998)
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