Dynamo Scaling Laws and Applications to the Planets

Christensen, Ulrich R.

doi:10.1007/978-1-4419-5901-0_17

Cited by 15 publications

(22 citation statements)

References 52 publications

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“…However, while for the nominal core size the observed dipole moment is obtained with a plausible value of the buoyancy flux, this is hardly possible with a much smaller core. The field strength B inside the dynamo scales with the buoyancy flux per unit area according to B / ðFq B Þ 1=3 (Christensen, 2010), where F is an 'efficiency factor', that is proportional to both g and D, hence to r 2 c . For a given value of the dipole moment the dipole field strength at the surface of the core (and presumably also the mean field strength inside the core) varies as B / r À3 c .…”

Section: Discussionmentioning

confidence: 99%

“…The basis for re-scaling magnetic field strength is the finding that for dipolar dynamos the field strength is nearly independent of rotation rate and viscosity and varies with the cubic root of the power generated by buoyancy forces (Christensen and Aubert, 2006;Aubert et al, 2009;Christensen, 2010). In numerical dynamo models this holds aside from a correction factor that accounts for the fraction of energy flux that is not dissipated by Joule heating (which in planets is assumed to be small).…”

Section: Scaling To Ganymedementioning

confidence: 98%

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Iron snow dynamo models for Ganymede

Christensen

2015

Icarus

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Section: Discussionmentioning

confidence: 99%

Section: Scaling To Ganymedementioning

confidence: 98%

Iron snow dynamo models for Ganymede

Christensen

2015

Icarus

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“…Although we are going to discuss these two problems in some detail, our main objective in this paragraph is not to provide a specialised review of any of them either, but rather to highlight some important trends and phenomenological aspects of these problems that relate to what we have discussed so far, and to the broader study of large-scale dynamos. Readers interested in specialised reviews are encouraged to consult Brandenburg & Subramanian (2005 a ), Charbonneau (2010), Miesch (2012), Charbonneau (2014), Brun & Browning (2017) and Brandenburg (2018) on solar and stellar dynamos and Christensen (2010), Jones (2011) and Roberts & King (2013) on geo- and planetary dynamos.…”

Section: The Diverse Challenging Complexity Of Large-scale Dynamosmentioning

confidence: 99%

“…Readers more specifically interested in relatively recent developments on astrophysical and planetary dynamo problems may notably want to consult the reviews by Christensen (2010), Jones (2011), Roberts & King (2013) on geo- and planetary dynamos, Charbonneau (2010), Miesch (2012), Charbonneau (2014), Brun & Browning (2017), Brandenburg (2018) on solar and stellar dynamos, Shukurov (2007), Brandenburg (2015) on galactic dynamos, Kulsrud & Zweibel (2008), Widrow et al. (2012), Durrer & Neronov (2013), Subramanian (2019) on cosmic and primordial magnetic fields and Federrath (2016) on dynamos in highly compressible astrophysical flows.…”

Section: Mhd Astrophysical Fluid Dynamics and Plasma Physics Textbooksmentioning

confidence: 99%

Dynamo theories

2019

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These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids and plasmas, blended with a review of current research in the field. The primary focus is on the physical and mathematical concepts underlying different (turbulent) branches of dynamo theory, with some astrophysical, geophysical and experimental contexts disseminated throughout the document. The text begins with an introduction to the rationale, observational and historical roots of the subject, and to the basic concepts of magnetohydrodynamics relevant to dynamo theory. The next two sections discuss the fundamental phenomenological and mathematical aspects of (linear and nonlinear) small- and large-scale magnetohydrodynamic (MHD) dynamos. These sections are complemented by an overview of a selection of current active research topics in the field, including the numerical modelling of the geo- and solar dynamos, shear dynamos driven by turbulence with zero net helicity and MHD-instability-driven dynamos such as the magnetorotational dynamo. The difficult problem of a unified, self-consistent statistical treatment of small- and large-scale dynamos at large magnetic Reynolds numbers is also discussed throughout the text. Finally, an excursion is made into the relatively new but increasingly popular realm of magnetic-field generation in weakly collisional plasmas. A short discussion of the outlook and challenges for the future of the field concludes the presentation.

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“…Several scaling laws have been proposed to explain the various strengths of planetary magnetic fields (see review by Christensen (2010)), among which the scaling law relating field strength to the energy flux proposed by Christensen et al (2009) can fit most planets but also fast-rotating stars. While these scaling laws have been derived for convection-driven dynamos, the physical principles on which they are based (Christensen, 2010) remain largely valid also for mechanically driven dynamos.…”

Section: Introductionmentioning

confidence: 99%