We propose new scaling laws for the properties of planetary dynamos. In
particular, the Rossby number, the magnetic Reynolds number, the ratio of
magnetic to kinetic energy, the Ohmic dissipation timescale and the
characteristic aspect ratio of the columnar convection cells are all predicted
to be power-law functions of two observable quantities: the magnetic dipole
moment and the planetary rotation rate. The resulting scaling laws constitute a
somewhat modified version of the scalings proposed in Christensen & Aubert
(2006) and Christensen (2010). The main difference is that, in view of the
small value of the Rossby number in planetary cores, we insist that the
nonlinear inertial term, (u.grad)u, is negligible. This changes the exponents
in the power-laws which relate the various properties of the fluid dynamo to
the planetary dipole moment and rotation rate. Our scaling laws are consistent
with the available numerical evidence.
%0 Generic
%1 citeulike:12103879
%A Davidson, P. A.
%D 2013
%K imported
%T Scaling Laws for Planetary Dynamos
%U http://arxiv.org/abs/1302.7140
%X We propose new scaling laws for the properties of planetary dynamos. In
particular, the Rossby number, the magnetic Reynolds number, the ratio of
magnetic to kinetic energy, the Ohmic dissipation timescale and the
characteristic aspect ratio of the columnar convection cells are all predicted
to be power-law functions of two observable quantities: the magnetic dipole
moment and the planetary rotation rate. The resulting scaling laws constitute a
somewhat modified version of the scalings proposed in Christensen & Aubert
(2006) and Christensen (2010). The main difference is that, in view of the
small value of the Rossby number in planetary cores, we insist that the
nonlinear inertial term, (u.grad)u, is negligible. This changes the exponents
in the power-laws which relate the various properties of the fluid dynamo to
the planetary dipole moment and rotation rate. Our scaling laws are consistent
with the available numerical evidence.
@misc{citeulike:12103879,
abstract = {{We propose new scaling laws for the properties of planetary dynamos. In
particular, the Rossby number, the magnetic Reynolds number, the ratio of
magnetic to kinetic energy, the Ohmic dissipation timescale and the
characteristic aspect ratio of the columnar convection cells are all predicted
to be power-law functions of two observable quantities: the magnetic dipole
moment and the planetary rotation rate. The resulting scaling laws constitute a
somewhat modified version of the scalings proposed in Christensen \& Aubert
(2006) and Christensen (2010). The main difference is that, in view of the
small value of the Rossby number in planetary cores, we insist that the
nonlinear inertial term, (u.grad)u, is negligible. This changes the exponents
in the power-laws which relate the various properties of the fluid dynamo to
the planetary dipole moment and rotation rate. Our scaling laws are consistent
with the available numerical evidence.}},
added-at = {2019-03-25T08:20:55.000+0100},
archiveprefix = {arXiv},
author = {Davidson, P. A.},
biburl = {https://www.bibsonomy.org/bibtex/261dd5e1f96d3e7dea053cec95ec364b4/ericblackman},
citeulike-article-id = {12103879},
citeulike-linkout-0 = {http://arxiv.org/abs/1302.7140},
citeulike-linkout-1 = {http://arxiv.org/pdf/1302.7140},
day = 28,
eprint = {1302.7140},
interhash = {0de94230f33e30ba0b867eca8e1c1e01},
intrahash = {61dd5e1f96d3e7dea053cec95ec364b4},
keywords = {imported},
month = feb,
posted-at = {2013-03-04 04:39:20},
priority = {2},
timestamp = {2019-03-25T08:20:55.000+0100},
title = {{Scaling Laws for Planetary Dynamos}},
url = {http://arxiv.org/abs/1302.7140},
year = 2013
}