Instability of non-linear α2-dynamos

Fearn, David R.; Rahman, M.M.

doi:10.1016/j.pepi.2003.12.010

Cited by 3 publications

(1 citation statement)

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“…α 0 = 25), the stronger forcing results in a large and rapidly growing magnetic field and ultimately in numerical instability. Although we have not investigated the source of the instability in detail, the issue may be specific to the axisymmetric problem we are studying, as in fully 3D models more powerful equilibration limits the magnetic field strength (Fearn and Rahman 2004b).…”

Section: Magnitude Of αmentioning

confidence: 99%

The inherent instability of axisymmetric magnetostrophic dynamo models

Hardy

Livermore

Niesen

2022

Geophysical & Astrophysical Fluid Dynamics

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Recent studies have demonstrated the possibility of constructing magnetostrophic dynamo models, which describe the slowly evolving background state of Earth's magnetic field when inertia and viscosity are negligible. Here we explore the properties of steady, stable magnetostrophic states as a leading order approximation to the slow dynamics within Earth's core. For the case of an axisymmetric magnetostrophic system driven by a prescribed α-effect, we confirmed the existence of four known steady states: ±B d , ±B q , where B d is purely dipolar and B q is purely quadrupolar. Importantly, here we show that in all but the most weakly driven cases, an initial magnetic field that is not purely dipolar or quadrapolar never converges to these states. Despite this instability, we also show that there are a plethora of instantaneous solutions that are quasi-steady, but nevertheless unstable. If the dynamics in Earth's core are reasonably modelled by a strongly driven α-effect, this work suggests that the background state can never be steady. We discuss the difficulties in comparing our magnetostrophic models with geomagnetic timeseries.

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Section: Magnitude Of αmentioning

confidence: 99%