Abstract
SUMMARY We present a method to estimate the typical magnitude of flow close to Earth's core surface based on observational knowledge of the geomagnetic main field (MF) and its secular variation (SV), together with prior information concerning field-flow alignment gleaned from numerical dynamo models. An expression linking the core surface flow magnitude to spherical harmonic spectra of the MF and SV is derived from the magnetic induction equation. This involves the angle γ between the flow and the horizontal gradient of the radial field. We study γ in a suite of numerical dynamo models and discuss the physical mechanisms that control it. Horizontal flow is observed to approximately follow contours of the radial field close to high-latitude flux bundles, while more efficient induction occurs at lower latitudes where predominantly zonal flows are often perpendicular to contours of the radial field. We show that the amount of field-flow alignment depends primarily on a magnetic modified Rayleigh number Raη=αg0ΔTD/ηΩ, which measures the vigour of convective driving relative to the strength of magnetic dissipation. Synthetic tests of the flow magnitude estimation scheme are encouraging, with results differing from true values by less than 8 per cent. Application to a high-quality geomagnetic field model based on satellite observations (the xCHAOS model in epoch 2004.0) leads to a flow magnitude estimate of 11–14 km yr−1, in accordance with previous estimates. When applied to the historical geomagnetic field model gufm1 for the interval 1840.0–1990.0, the method predicts temporal variations in flow magnitude similar to those found in earlier studies. The calculations rely primarily on knowledge of the MF and SV spectra; by extrapolating these beyond observed scales the influence of small scales on flow magnitude estimates is assessed. Exploring three possible spectral extrapolations we find that the magnitude of the core surface flow, including small scales, is likely less than 50 km yr−1.
Highlights
Flow of electrically conducting fluid in the Earth’s liquid outer core generates the geomagnetic field via motional induction
Because we are mostly interested in magnetic field evolution on time-scales short compared to the magnetic diffusion time, and because we will later apply our method to observations of the geomagnetic field, we focused on dipole-dominated non-reversing dynamos
It seems intuitively reasonable that a magnetic modified Rayleigh number Raη, which is the modified Rayleigh number Ra with ν replaced by η, will be of relevance in rapidly rotating, convection-driven dynamos.∗ We will show later that Raη turns out to be very useful when investigating the average amount of field-flow alignment and that it may be related to the efficiency of induction in numerical dynamo models
Summary
Flow of electrically conducting fluid in the Earth’s liquid outer core generates the geomagnetic field via motional induction. To our knowledge the only previous study of field-flow alignment in numerical models of the geodynamo was that by Takahashi & Matsushima (2005) They observed that as the convective forcing (measured by the Rayleigh number Ra) was increased, less flow perpendicular to field lines occurred, the dynamos became less efficient, and there was a reduction in magnetic energy. In this investigation we focus on field-flow alignment close to the outer boundary and on extracting the information required by our flow magnitude estimation scheme.
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