2017 # Transition to Turbulent Dynamo Saturation

**Abstract:** 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). Extrapolating such viscous scaling-laws to realistic parameter values leads to an underestimation of the magnetic energy by several orders of magnitude. The origin of this discrepancy is that fully 3D DNS cannot reach low enough values of the magnetic Prandtl number Pm. To bypass this limitation and investigate dynamo saturation at very…

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“…We can summarize the findings of Seshasayanan et al (2017) and of the present study as follows: geostrophic base flows lead to the inertial scaling regime, with B 2 independent of the rotation rate, whereas base flows that are not in geostrophic balance can achieve the magneto-geostrophic scaling regime, with much larger magnetic energy, proportional to the global rotation rate. In spherical geodynamo simulations, which criterion should be retained to observe a ν-independent scaling regime -and whether this scaling-law involves the global rotation rate -may depend on the region of the sphere that contributes most to magnetic-field generation.…”

confidence: 63%

“…We can summarize the findings of Seshasayanan et al (2017) and of the present study as follows: geostrophic base flows lead to the inertial scaling regime, with B 2 independent of the rotation rate, whereas base flows that are not in geostrophic balance can achieve the magneto-geostrophic scaling regime, with much larger magnetic energy, proportional to the global rotation rate. In spherical geodynamo simulations, which criterion should be retained to observe a ν-independent scaling regime -and whether this scaling-law involves the global rotation rate -may depend on the region of the sphere that contributes most to magnetic-field generation.…”

confidence: 63%

“…As opposed to standard weakly nonlinear methods (Nunez et al 2001;Seshasayanan et al 2017), our study is based on scale separation only and is not restricted to the immediate vicinity of the dynamo threshold. We therefore studied the scaling behavior of the magnetic energy at large distance from threshold: when both the Reynolds number and magnetic Reynolds number are large, the magnetic energy is independent of both viscosity and magnetic diffusivity.…”

confidence: 99%

“…Again, the determination of through fully 3-D DNS remains prohibitively expensive at large and low . Instead, the existence of FAIs, as well as whether and when a forward energy cascade develops, could be investigated through nonlinear extensions of this work: one could design a weakly nonlinear model by keeping only the first unstable vertically dependent mode and its feedback onto the 2-D base flow, in the spirit of Benavides & Alexakis (2017) and Seshasayanan, Gallet & Alexakis (2017). For physical systems that are amenable to 3-D DNS in extreme parameter regimes, models of this kind have predictive skills when compared to 3-D DNS, at least at a qualitative level (van Kan & Alexakis 2019).…”

confidence: 99%