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Stratified precessional flow in spherical geometry

Published online by Cambridge University Press:  08 February 2013

Xing Wei  and
Andreas Tilgner
Xing Wei*
Affiliation:
Institute of Geophysics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
Andreas Tilgner
Affiliation:
Institute of Geophysics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
*
†Email address for correspondence: Xing.Wei@phys.uni-goettingen.de
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Abstract

We investigate numerically, in spherical geometry, the interaction of stratification with precession. Both stable stratification and unstable stratification are studied. In the parameter regime we are concerned with, stable stratification suppresses the precessional instability, whereas unstable stratification and precession can either stabilize or destabilize each other at different precession rates.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Stratified flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , R2
Copyright
©2013 Cambridge University Press

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References

Bullard, E. C. 1949 The magnetic field within the Earth. Proc. R. Soc. A 197, 433–453.Google Scholar
Busse, F. H. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739–751.CrossRefGoogle Scholar
Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.CrossRefGoogle Scholar
Busse, F. H. 2000 Homogeneous dynamos in the planetary cores and in the laboratory. Annu. Rev. Fluid Mech. 32, 383–408.CrossRefGoogle Scholar
Dwyer, C. A., Stevenson, D. J. & Nimmo, F. 2011 A long-lived lunar dynamo driven by continuous mechanical stirring. Nature 479, 212–215.CrossRefGoogle ScholarPubMed
Greenspan, H. P. 1968 The Theory of Rotating Fluids, 1st edn. Cambridge University Press.Google Scholar
Jones, C. A. 2011 Planetary magnetic fields and fluid dynamos. Annu. Rev. Fluid Mech. 43, 583–614.CrossRefGoogle Scholar
Kerswell, R. 1993 Elliptical instabilities of stratified hydromagnetic waves. Geophys. Astrophys. Fluid Dyn. 71, 105–143.CrossRefGoogle Scholar
Kerswell, R. 1995 On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers. J. Fluid Mech. 298, 311–325.CrossRefGoogle Scholar
Le Bars, M. & Le Dizés, S. 2006 Thermo-elliptical instability in a rotating cylindrical shell. J. Fluid Mech. 563, 189–198.CrossRefGoogle Scholar
Le Bars, M., Wieczorek, M. A., Karatekin, O., Cébron, D. & Laneuville, M. 2011 An impact-driven dynamo for the early Moon. Nature 479, 215–218.CrossRefGoogle ScholarPubMed
Lorenzani, S. & Tilgner, A. 2001 Fluid instabilities in precessing spheroidal cavities. J. Fluid Mech. 447, 111–128.CrossRefGoogle Scholar
Lorenzani, S. & Tilgner, A. 2003 Inertial instabilities of fluid flow in precessing spheroidal shells. J. Fluid Mech. 492, 363–379.CrossRefGoogle Scholar
Malkus, V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 160, 259–264.CrossRefGoogle ScholarPubMed
Noir, J., Brito, D., Aldridge, K. & Cardin, P. 2001 Experimental evidence of inertial waves in a precessing spheroidal cavity. Geophys. Res. Lett. 28, 3785–3788.CrossRefGoogle Scholar
Poincaré, H. 1910 Sur la précession des corps déformables. Bull. Astron. 27, 321–356.CrossRefGoogle Scholar
Roberts, P. H. 1968 On the thermal instability of a rotating-fluid sphere containing heat sources. Phil. Trans. R. Soc. Lond. A 263, 93–117.Google Scholar
Roberts, P. H. & Glatzmaier, G. A. 2000 Geodynamo theory and simulations. Rev. Mod. Phys. 72, 1081–1123.CrossRefGoogle Scholar
Tilgner, A. 1999a Magnetohydrodynamic flow in precessing spherical shells. J. Fluid Mech. 379, 303–318.CrossRefGoogle Scholar
Tilgner, A. 1999b Spectral methods for the simulation of incompressible flows in spherical shells. Intl J. Numer. Meth. Fluids 30, 713–724.3.0.CO;2-Y>CrossRefGoogle Scholar
Tilgner, A. 2005 Precession driven dynamo. Phys. Fluids 17, 034104.CrossRefGoogle Scholar
Tilgner, A. & Busse, F. H. 1997 Finite-amplitude convection in rotating spherical fluid shells. J. Fluid Mech. 332, 359–376.CrossRefGoogle Scholar
Tilgner, A. & Busse, F. H. 2001 Fluid flows in precessing spherical shells. J. Fluid Mech. 426, 387–396.CrossRefGoogle Scholar
Vanyo, J. & Likins, P. 1971 Measurement of energy dissipation in a liquid-filled, precessing, spherical cavity. Trans. ASME: J. Appl. Mech. 38, 674–682.CrossRefGoogle Scholar
Weiss, B. P., Berdahl, J. S., Tanton, L. E., Stanley, S., Lima, E. A. & Carporzen, L. 2008 Magnetism on the angrite parent body and the early differentiation of planetesimals. Science 322, 713–716.CrossRefGoogle ScholarPubMed
Wicht, J. & Tilgner, A. 2010 Theory and modelling of planetary dynamos. Space Sci. Rev. 152, 501–542.CrossRefGoogle Scholar
Zhang, K., Liao, X. & Busse, F. H. 2007 Asymptotic solutions of convection in rapidly rotating no-slip spheres. J. Fluid Mech. 578, 371–380.CrossRefGoogle Scholar