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, 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 1โฉฝRe๐โฉฝ250, 0ยฐโฉฝฮธโฉฝ90ยฐ, and 1โฉฝfโฉฝ3. The results suggest that, at the lowest Re๐Reฯ investigated, the magnetic field has a negligible impact on the evolution of the turbulence kinetic energy ๐ธ๐. At higher Re๐ 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 ๐ธ๐ shows the opposite trend, being rapidly driven from its initial values to essentially
zero very early in the transient at lower Re๐ values, while higher Re๐ values significantly retard this decay. An enhancement of density fluctuations is
noted in the intermediate Re๐ range. An interesting observation pertaining to the normalized cross helicity is
the fast decay to zero of this quantity when Re๐=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 ๐ธ๐ decay mode is less sensitive to the value of ฮธ than that of ๐ธ๐. The relative contribution of ๐ธ๐,๐ธ๐, and the internal energy ๐ธ๐ to the total energy ๐ธ๐ก is discussed in relation to the values of f, ฮธ, and Re๐.
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