27 July 2015 to 21 August 2015
Nordita, Stockholm
Europe/Stockholm timezone

Dependence of magnetic dissipation on magnetic Prandtl number

12 Aug 2015, 11:35
25m
FD5 (FD5)

FD5

FD5

Oral Workshop, August 10-14 Pre-noon III

Speaker

Prof. Axel Brandenburg (Nordita)

Description

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 the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one- dimensional passive 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. For many astrophysical systems, the microscopic energy dissipation mechanism is not of Spitzer type, as assumed here. It is not obvious how this would affect our results. Unfortunately, the question of energy dissipation is not routinely examined in astrophysical fluid dynamics, nor is it always easy to determine energy dissipation rates, because many astrophysical fluid codes ignore explicit dissipation and rely entirely on numerical prescriptions needed to dissipate energy when and where needed. Our present work highlights once again that this can be a questionable procedure, because it means that even non-dissipative aspects, such as the strength of the dynamo which is characterized by the work done against the Lorentz force, are then ill-determined.

Primary author

Prof. Axel Brandenburg (Nordita)

Presentation materials