Electrodynamics of turbulent fluids with fluctuating electric conductivity (1911.06611v3)

Abstract: The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field is increased. If the fluctuations of conductivity and flow are correlated in a certain direction then an additional diamagnetic pumping effect results transporting magnetic field in opposite direction to the resistivity flux vector $\langle \eta'\vec{u}'\rangle$. Even for homogeneous turbulence fields in the presence of rotation an alpha effect appears. With the characteristic values of the outer core of the Earth or the solar convection zone, however, the dynamo number of the alpha effect never reaches supercritical values to operate as an $\alpha^2$-dynamo.

• The paper demonstrates that fluctuating electric conductivity substantially reduces turbulence-induced magnetic diffusivity, extending decay times for large-scale magnetic fields.
• The paper employs advanced mathematical models and direct numerical simulations via the Pencil Code to validate predictions of diamagnetic pumping and modified α effects.
• The paper reveals that conductivity-velocity correlations under rotation induce new dynamo effects, offering valuable insights for understanding Earth and astrophysical magnetic phenomena.

Electrodynamics of Turbulent Fluids with Fluctuating Electric Conductivity

The paper "Electrodynamics of Turbulent Fluids with Fluctuating Electric Conductivity" by Rüdiger, Küker, and Käpylä examines the influence of fluctuating electric conductivity on mean-field electrodynamics in turbulent fluids. The research addresses the interactions involving conductivity fluctuations and their correlation with fluid velocity, contributing to nuanced understandings of turbulence-originated magnetic diffusivity, diamagnetic pumping effects, and the appearance of new dynamo effects.

The observation that fluctuating electric conductivity could impact large-scale magnetic fields is central to the paper. When fluctuations in conductivity are uncorrelated with velocity, the result is primarily a reduced turbulence-induced magnetic diffusivity. This leads to an increased decay time for large-scale magnetic fields and cycle times in oscillating turbulent dynamo models. However, when fluctuations in conductivity are correlated with fluid motion in a specific direction, additional phenomena are predicted, notably diamagnetic pumping, where the magnetic field is transported opposite to the direction of diffusivity flux.

Under conditions of global rotation, and even within homogeneous turbulence fields, a novel $\alpha$ effect emerges. However, the dynamo number linked to the $\alpha$ effect under realistic conditions (applicable to the Earth's outer core or the solar convection zone settings) doesn't achieve the supercritical values required for an $\alpha^2$ dynamo, though oscillating $\alpha$ dynamos with differential rotation remain feasible.

The paper provides detailed mathematical formulations and derivations to support these claims. Specifically, the interaction of fluctuating diffusivity with the rotationally influenced turbulence field is modeled using advanced mathematical frameworks and numerical simulations via direct numerical schemes executed by the tailored MHD code, "Pencil Code." These simulations provided concrete evidence for theoretical predictions, reflecting reduced effective eddy diffusivity and validating the proposed theoretical framework.

Key numerical results reflect the paper's findings. Numerical simulations demonstrated that the presence of conductivity fluctuations yields reduced effective magnetic diffusivity, confirming theoretical predictions that these effects disappear in the high-conductivity limit for large magnetic Reynolds numbers. The factorization of rotational and diffusivity interactions suggests potential dynamo models wherein conductivity fluctuations systematically influence secondary flow structures.

The implications of these insights are promising both in astrophysical contexts and earth sciences. For the Earth's outer core and solar convection zone, understanding such conductivity and rotation-induced effects is crucial for explaining observed magnetic phenomena. Practically, future studies could expand on this groundwork by probing conditions under which the conductivity’s correlation with velocity can be maximized or manipulated to observe or simulate specific magnetic field behaviors.

Theoretical considerations hint at broader applicability, perhaps among varied astrophysical and engineering systems where similar conductive and rotatory dynamics exist. Future research might explore scaling these principles to explore large-scale planetary or stellar dynamo actions and try to simulate or mathematically capture the multi-dimensional fluid and magnetic interactions.

In sum, while the $\alpha$ effect generated in this context doesn't immediately translate into a viable model for all dynamo types, it provides a basis for studying complex fluid and magnetic interactions in rotating systems with fluctuating properties. Understanding these complex systems enhances fundamental knowledge in physics and engineering applications, potentially leading to new technological methods for magnetic field manipulation in fluids.