Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T13:20:05.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Inertial–Alfvén waves as columnar helices in planetary cores

Published online by Cambridge University Press:  16 September 2016

O. P. Bardsley Open the ORCID record for O. P. Bardsley [Opens in a new window]  and
P. A. Davidson
O. P. Bardsley*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
P. A. Davidson
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a rapidly rotating, Boussinesq fluid stirred by buoyant anomalies. In such a system it is known that, in the absence of a magnetic field, inertial waves whose wave vectors lie normal to the rotation axis play a key role in establishing quasi-geostrophic motion. In particular, buoyant anomalies radiate low-frequency inertial wave packets which disperse along the rotation axis, leading to axially elongated columnar vortices. Here we focus on the influence of an ambient magnetic field on this process, motivated by the dynamics of planetary cores. We find that, once again, the waves responsible for establishing quasi-geostrophic structures have wave vectors normal to the rotation axis; however, these are not conventional inertial waves, but rather hybrid ‘inertial–Alfvén waves’. Their frequency equals that of an Alfvén wave but their axial group velocity is half that of the equivalent inertial wave. They have maximal kinetic, magnetic and cross-helicity, carry magnetic and kinetic energy in equal amounts, and are particularly potent in establishing columnar, helical vortices through the spontaneous emission of axially elongated wave packets. Although our hybrid inertial–Alfvén waves have been overlooked in dynamo literature to date, we speculate that they in fact play a central role in planetary dynamos.

JFM classification

Geophysical and Geological Flows: Geodynamo Geophysical and Geological Flows: Quasi-geostrophic flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , R2
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Braginsky, S. I. 1967 Magnetic waves in the Earth’s core. Geomagn. Aeron. 7, 851–859.Google Scholar
Christensen, U. R. 2011 Geodynamo models: tools for understanding properties of Earth’s magnetic field. Phys. Earth Planet. Inter. 187 (3–4), 157–169.CrossRefGoogle Scholar
Chulliat, A., Loper, D. E. & Shimizu, H. 2004 Buoyancy-driven perturbations in a rapidly rotating, electrically conducting fluid. Part III: effect of the Lorentz force. Geophys. Astrophys. Fluid Dyn. 98 (6), 507–535.CrossRefGoogle Scholar
Davidson, P. A. 2013 Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Cambridge University Press.CrossRefGoogle Scholar
Davidson, P. A. 2014 The dynamics and scaling laws of planetary dynamos driven by inertial waves. Geophys. J. Intl 198 (3), 1832–1847.CrossRefGoogle Scholar
Davidson, P. A. & Ranjan, A. 2015 Planetary dynamos driven by helical waves – II. Geophys. J. Intl 202 (3), 1646–1662.CrossRefGoogle Scholar
Davidson, P. A., Staplehurst, P. J. & Dalziel, S. B. 2006 On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144.CrossRefGoogle Scholar
Finlay, C. C., Dumberry, M., Chulliat, A. & Pais, M. A. 2010 Short timescale core dynamics: theory and observations. Space Sci. Rev. 155 (1–4), 177–218.CrossRefGoogle Scholar
Hide, R. 1966 Free hydromagnetic oscillations of the Earth’s core and the theory of the geomagnetic secular variation. Phil. Trans. R. Soc. Lond. A 259 (1107), 615–647.Google Scholar
Jault, D. 2008 Axial invariance of rapidly varying diffusionless motions in the Earth’s core interior. Phys. Earth Planet. Inter. 166 (1–2), 67–76.CrossRefGoogle Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Moffatt, H. K. & Loper, D. E. 1994 The magnetostrophic rise of a buoyant parcel in the Earth’s core. Geophys. J. Intl 117 (2), 394–402.CrossRefGoogle Scholar
Olson, P., Christensen, U. & Glatzmaier, G. A. 1999 Numerical modeling of the geodynamo: mechanisms of field generation and equilibration. J. Geophys. Res. Solid Earth 104 (B5), 10383–10404.CrossRefGoogle Scholar
St Pierre, M. G. 1996 On the local nature of turbulence in Earth’s outer core. Geophys. Astrophys. Fluid Dyn. 83 (3–4), 293–306.CrossRefGoogle Scholar