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Extrapolating such viscous scaling laws to realistic parameter values leads to an underestimation of the magnetic energy by several orders of magnitude. While the saturated magnetic energy is independent of viscosity in dynamo experiments, it remains viscosity dependent in state-of-the-art 3D direct numerical simulations (DNS). Transition to Turbulent Dynamo Saturation. The transition to the turbulent saturation regime occurs at a low value of the magnetic Prandtl number, Pm ≃10-3, which explains why it has been overlooked by numerical studies so far. We show that the magnetic energy transitions from a high-Pm viscous scaling regime to a low-Pm turbulent scaling regime, the latter being independent of viscosity. This parameter regime is currently out of reach to fully 3D DNS. We perform numerical simulations of the resulting set of reduced equations for Pm down to 2 Ã-10-5. To bypass this limitation and investigate dynamo saturation at very low Pm, we focus on the vicinity of the dynamo threshold in a rapidly rotating flow: the velocity field then depends on two spatial coordinates only, while the magnetic field consists of a single Fourier mode in the third direction. The origin of this discrepancy is that fully 3D DNS cannot reach low enough values of the magnetic Prandtl number Pm. Seshasayanan, Kannabiran Gallet, Basile Alexakis, Alexandros Transition to Turbulent Dynamo Saturation With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.
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The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. Schober, J Schleicher, D R G Federrath, C Bovino, S Klessen, R S