Evidence for Turbulent Magnetic Diffusion in Earth's Core

Abstract

Turbulent flow in Earth's liquid core is thought to be responsible for generating the geomagnetic field. The same fluid motion may also contribute to the destruction of the magnetic field by enhancing the effects of magnetic diffusion. Investigations of both processes have a long history (e.g., Moffatt, 1978). Parker (1955) was the first to recognize the importance of "cyclonic" events in generating magnetic field. Such helical flow is now associated with the α-effect in the context of mean-field theory (Krause & Rädler, 1980). Turbulent magnetic diffusion also falls within the scope of mean-field theory. Early studies proposed a formal equivalence between the diffusion of a magnetic field and a passive scalar (e.g., Parker, 1971). This view was later challenged by Moffatt (1974) using a Lagrangian description of turbulent flow in a perfectly conducting fluid. Supporting arguments by Kraichnan (1976a) drew attention to the role of helicity fluctuations in the diffusion of magnetic fields. This behavior was taken as evidence that turbulent diffusion of magnetic fields and passive scalars were not perfectly analogous.Mean-field theory provides a framework for quantifying the effects of turbulence on magnetic diffusion. This theory is however limited, due to the neglect of feedbacks of the magnetic field on fluid motion. Further, it relies on a simplifying assumption, sometimes called first-order smoothing, where non-linear terms are neglected. Formal justification of this approximation requires the correlation time of the fluid motion to be short compared with overturn time of the largest eddies (Knobloch, 1977). Extensions to the theory (Kraichnan, 1976a) and numerical simulations (Kraichnan, 1976b;Sur et al., 2008) show that mean-field theory can be adapted to include velocity correlation times in the range of the overturn time. Comparable overturn and correlation times are expected for the case of high-Reynolds-number flows.

A field theory approach to the statistical kinematic dynamo

“…If the turbulent flow's lengthscale were to correspond to the dissipation lengthscale, Rm t could be as low as Rm t ∼ 1 [13]. Holdenried-Chernoff and Buffett [46] found that a local Rm t based on the eddy dissipation lengthscale might be an order of magnitude smaller than the global Rm, so we might expect Rm t < 100 at the lengthscales relevant to the turbulent flow. These are quite moderate values, so if we wanted to consider the turbulent diffusivity in the context of the geodynamo we should probably use the more general expression (50).…”

“…Let us now look for the poles of g(k, ω) by solving g −1 (ω * , k) = 0 for ω * (k). From (46) we see that they must occur when…”

“…The correlation function for the fluid velocity in the Earth's core is unknown, as are its correlation length and time. These parameters may however be estimated through scaling arguments and extrapolations from geodynamo simulations [13,46], and appear to be on the order ℓ ∼ 10 5 m and τ ∼ 10 2 years, which is short compared to convective overturn times of ∼150 years. Throughout this paper, the convention will be to denote the arguments of functions using parentheses (e.g.…”

“…A number of studies [18,19,[43][44][45] have shown that, using current estimates for the core's molecular magnetic diffusivity, the time correlations of the magnetic field decay more rapidly than expected for a purely dipolar decay. Davis and Buffett [20] concluded that this rapid decay is not due to a contribution from higher order decay modes, implying that the higher magnetic diffusivity observed in the paleomagnetic record could be attributed to an enhancement of the magnetic diffusivity due to turbulent fluid effects [46]. In this case, the ability to physically link statistical properties of the magnetic and velocity fields under different assumptions allows us to infer core-properties that are not directly observable, such as the ensemble averaged root-mean squared velocity in the bulk of the outer core.…”

Asymmetric Dipole Trends in Geodynamo Models and the Paleomagnetic Field

“…This value is slightly less than half the dipole decay time expected for the molecular diffusivity adopted in the geodynamo models ( η = 0.8 m 2 s −1 ). The difference is attributed to the effects of turbulent diffusion (Holdenried‐Chernoff & Buffett, 2022). The upper and lower limits on A are set by matching the mean and standard deviation of x ( t ) for Case B3.…”