Dynamo Scaling Laws and Applications to the Planets

By U. Christensen. 2010

269 citations recorded by the source corpus.

Scaling laws for planetary dynamos relate the characteristic magnetic field strength, characteristic flow velocity and other properties to primary quantities such as core size, rotation rate, electrical conductivity and heat flux. Many different scaling laws have been proposed, often relying on the assumption of a balance of Coriolis force and Lorentz force in the dynamo. Their theoretical foundation is reviewed. The advent of direct numerical simulations of planetary dynamos and the ability to perform them for a sufficiently wide range of control parameters allows to test the scaling laws. The results support a magnetic field scaling that is not based on a force balance, but on the energy flux available to balance ohmic dissipation. In its simplest form, it predicts a field strength that is independent of rotation rate and electrical conductivity and proportional to the cubic root of the available energy flux. However, rotation rate controls whether the magnetic field is dipolar or multipolar. Scaling laws for velocity, heat transfer and ohmic dissipation are also discussed. The predictions of the energy-based scaling law agree well with the observed field strength of Earth and Jupiter, but for other planets they are more difficult to test or special pleading is required to explain their field strength. The scaling law also explains the very high field strength of rapidly rotating low-mass stars, which supports its rather general validity.

Subfields: Astronomy and Astrophysics, Molecular Biology, Physiology

View Paper: https://www.semanticscholar.org/paper/6f4991a07596c09318f231621771c314fdbeffc4

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Citations in the corpus

Observations of Cool-Star Magnetic Fields (2012, background): “Young brown dwarfs can be expected to harbor substantial magnetic fields (Reiners and Christensen, 2010), and no fundamental difference is known to exist in the parameters that are believed to be relevant for magnetic flux generation between very-low mass stars and young brown dwarfs.”
Thermal evolution of the core with a high thermal conductivity (2014, unknown): “Both strategies have their merits and limits, in particular the fact that both the present CMB heat ﬂow (Lay et al., 2008) and Ohmic dissipation (Christensen, 2010) are poorly known, and the situation is of course worse for past periods.”
Turbulent geodynamo simulations: a leap towards Earth's core (2017, methodology): “This contrasts with previous studies, where the mean flow was subtracted or filtered out (Wicht and Christensen, 2010; Teed et al., 2014).”
Is Proxima Centauri b Habitable? A Study of Atmospheric Loss (2017, background): “As PCb rotates slower than the Earth (Ribas et al. 2016), this choice is consistent with certain dynamo scaling laws (Christensen 2010).”
Rotating convective turbulence in Earth and planetary cores (2015, background): “1d, that the flows in present day dynamo models can be extrapolated to planetary core settings (e.g., Christensen, 2010, 2011).”
Spherical convective dynamos in the rapidly rotating asymptotic regime (2016, methodology): “(2.20) We finally use a standard measure (Wicht & Christensen 2010; Teed et al. 2015) for the enforcement of the Taylor constraint (Taylor 1963), by assessing the cancellation level of the Lorentz force acting on axial cylinders: T (s) = ∫ z+ z− eϕ · (∇ × B) × B dz∫ z+ z− ∣∣∣∣ eϕ · (∇ × B) × B ∣∣∣∣…”