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The dynamics and scaling laws of planetary dynamos driven by inertial waves

Davidson, PA (2014) The dynamics and scaling laws of planetary dynamos driven by inertial waves. Geophysical Journal International, 198. pp. 1832-1847. ISSN 0956-540X

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Great progress has been made in the numerical simulation of planetary dynamos, though these numerical experiments still operate in a regime very far from the planets. For example, it seems unlikely that viscous forces are at all significant in planetary interiors, yet some of the simulations display a significant dependence on viscosity, and indeed in some of the simulations the dynamo mechanism is itself viscously driven, taking the form of helical Ekman pumping within columnar convection rolls. Given the similarity of the external magnetic fields observed in the terrestrial planets and gas giants, and the extremely small value of the Ekman number in all such cases, it seems natural to suppose that the underlying dynamo mechanism in these planets is simple, robust, independent of viscosity and insensitive to mechanical boundary conditions. A key step to identifying this mechanism is to determine the source of helicity in planetary cores, which itself should be robust, independent of viscosity and insensitive to boundary conditions. In this paper, we explore the possibility that the helicity in the core of the Earth arises from the spontaneous emission of inertial waves, driven by the equatorial heat flux in the outer core. We also ask if a similar mechanism might operate in other planets, and perhaps act to supplement the helicity driven by Ekman pumping in the (viscous) numerical simulations. We demonstrate that such waves do indeed produce the required helicity distribution outside the tangent cylinder. Moreover, we show that these waves inevitably propagate along the axis of the columnar vortices, and indeed they are the very mechanism by which the columnar vortices form in the first place and the means by which the columns subsequently evolve. We also calculate the emf induced by such axially propagating inertial waves and show that, in principle, this emf is sufficient to support a self-sustaining dynamo of the α 2 type. Finally, we derive the scaling laws for this kind of inertial-wave dynamo. We compare these predictions with the (imperfect) simulations, and also with what little we know about the Earth's core. The numerical experiments fall into two categories; the slowly rotating simulations which cannot sustain inertial waves at the small scales and the rapidly rotating (planet-like) ones which can. Our scaling laws are consistent with the latter class of simulations, and also with what we know about the Earth. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Item Type: Article
Divisions: Div A > Fluid Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:05
Last Modified: 21 Sep 2017 01:39