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Planetary dynamos driven by helical waves - II

Davidson, PA and Ranjan, A (2015) Planetary dynamos driven by helical waves - II. Geophysical Journal International, 202. pp. 1646-1662. ISSN 0956-540X

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© The Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved. In most numerical simulations of the Earth's core the dynamo resides outside the tangent cylinder and may be crudely classified as being of the α < sup > 2 < /sup > type. In this region the flow comprises a sea of thin columnar vortices aligned with the rotation axis, taking the form of alternating cyclones and anticyclones. The dynamo is thought to be driven by these columnar vortices within which the flow is observed to be highly helical, helicity being a crucial ingredient of planetary dynamos. As noted in Davidson, one of the mysteries of this dynamo cartoon is the origin of the helicity, which is observed to be positive in the south and negative in the north. While Ekman pumping at the mantle can induce helicity in some of the overly viscous numerical simulations, it is extremely unlikely to be a significant source within planets. In this paper we return to the suggestion of Davidson that the helicity observed in the less viscous simulations owes its existence to helical wave packets, launched in and around the equatorial plane where the buoyancy flux is observed to be strong. Here we show that such wave packets act as a potent source of planetary helicity, constituting a simple, robust mechanism that yields the correct sign for h north and south of the equator. Since such a mechanism does not rely on the presence of a mantle, it can operate within both the Earth and the gas giants. Moreover, our numerical simulations show that helical wave packets dispersing from the equator produce a random sea of thin, columnar cyclone/anticyclone pairs, very like those observed in the more strongly forced dynamo simulations. We examine the local dynamics of helical wave packets dispersing from the equatorial regions, as well as the overall nature of an α < sup > 2 < /sup > -dynamo driven by such wave packets. Our local analysis predicts the mean emf induced by helical waves, an analysis that rests on a number of simple approximations which are consistent with our numerical experiments, while our global analysis yields exact integral relationships between the mean emf induced by the wave packets and the large-scale dipole and azimuthal field. Combining these local and integral equations yields a kinematic model for an α < sup > 2 < /sup > -dynamo driven by helical waves. Order-of-magnitude estimates based on these equations suggest that such a dynamo is indeed feasible.

Item Type: Article
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:43
Last Modified: 21 Sep 2017 01:38