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 always 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 Alfvén kinks .