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Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratio
Using direct numerical simulations of three-dimensional hydromagnetic
turbulence, either with helical or non-helical forcing, we show that
the ratio of kinetic to magnetic energy dissipation always increases
with magnetic Prandtl number, i.e., the ratio of kinematic
viscosity to magnetic diffusivity.
This dependence can always be approximated by a power law, but the
exponent is not the same in all cases.
For non-helical turbulence at large magnetic Prandtl numbers, the
exponent is around 1/3, while for all other cases it is between
0.6 and 2/3.
Characterizing the dynamo efficiency by the magnetic energy dissipation,
we emphasize that our results imply a sensitivity of both small-scale
and large-scale dynamos on the microphysical dissipation process.
To understand this behavior, we also study shell models of turbulence
and one-dimensional passive scalar and active scalar models.
We conclude that the magnetic Prandtl number dependence is qualitatively
best reproduced in the one-dimensional model as a result of dissipation
via localized Alfven kinks.