Instability of Ekman-Hartmann Boundary Layers,
with application to the fluid flow near the Core-Mantle Boundary
Benoit Desjardinsa, Emmanuel Dormyb,c, Emmanuel Grenierd
a C.E.A./D.I.F., B.P. 12, 91680 Bruyères le Châtel, France.
b IPGP, 4 place Jussieu, F-75252, Paris, France
c C.N.R.S., France.
d U.M.P.A., E.N.S. Lyon, 46 allée d'Italie,
69364 Lyon Cedex 07, France.
Physics of the Earth and Planetary Interiors, Vol. 123-1, pp. 15-27, 2001
Abstract.
Our aim is to investigate the instability of mixed Ekman-Hartmann
boundary layers arising in rotating incompressible magnetohydrodynamics
flows in a parameter regime relevant to the Earth liquid core. We
perform a local study in a half space at a given co-latitude
$\theta \neq \pi/2$, and assume a mean dipolar
axial magnetic field with internal sources.
Instabilities are driven, for high enough Reynolds number,
by the quadratic term in the momentum equation.
Following the work of Lilly, we restrict our analysis to
the linearized growth phase. We describe the dependence of the
critical Reynolds number in terms of $\theta$ and Elsasser number
(measuring the relative strength of Lorentz
and Coriolis terms). It is found that no matter how large
the Elsasser number is, there exists a critical
band centered on the equator in which instabilities
can occur.
For geophysically relevant values of parameters, this band extends
over some 45 degrees away from the equator.
This study establishes the possiblity of boundary layer instabilities
near the core-mantle boundary.
Keywords: Core-Mantle boundary; Ekman-Hartmann layers; Earth core
dynamics.
WARNING:
Although the LaTeX file was sent to the journal, for some reason,
the paper was scanned there.
As a result, and despite our corrections to the proofs,
equations (8), (21), (A.1), (A.7), (A.11) and (A.13) are
incorrect as printed.
Other minor mistakes were also introduced in the text.
The paper was fully reprinted in P.E.P.I. 124 (2001).
We strongly recommend to use the second printing rather than the present one.