Dynamo action of the large scale flow in a precessing cylinder

Precession is a well known phenomenon that (in a very general sense) paraphrases the
temporal change of the orientation of the spin axis of rotating objects. In rotating celestial bodies
with liquid interior precession causes a volume force that directly drives a non-axisymmetric fluid
flow [1]. Paradigmatic example is the liquid core of the Earth [2], for which the forcing is
considerably strong due to the rather large angle between rotation axis and precession axis. An even
stronger forcing is assumed for the ancient moon three to four billion years ago [3]. Precessional
forcing of the fluid interior of planets or moons is of interest because the resulting internal flows in
terms of inertial modes or turbulence back-react on the rotation of the whole body, which may
become evident for example in length of day variations or periodic changes of the nutation angle.
Furthermore a precession-driven flow of an electrically conductive fluid is capable of generating a
large scale magnetic field [4]. From an energetic point of view, the directly driven non-
axissymmetric flow is not sufficient to generate a magnetic field [5], however, multifaceted
instabilities of the primary flow provide the possibility to extract a large a amount of kinetic energy
from the rotational fluid motions into a fluid flow, which may be more suitable of generating a
magnetic field via electromagnetic induction [6].
In order to investigate to what extent a precession-driven flow can power a dynamo, and what
properties the related magnetic field would have, an experiment is currently being constructed at
HZDR, in which 6 tons of liquid sodium will precess in a cylinder with 2 meters height and 2
meters in diameter [7]. The design of the experiment is attended by comprehensive numerical
simulations, which showed that at the edge of the transition between a complex but still laminar
flow to a fully developed turbulent state, onset of dynamo action can be expected [8]. This state of
flow is characterized by an almost complete transformation of the original rotation into large-scale
inertial waves and small-scale turbulent flow. The dynamo effect found in the simulations is mainly
due to an evolving axially symmetric flow component and the strong shear layer near the outer
walls due to the massive extraction of rotational energy [9]. Free inertial waves in the form of
triadic resonances as the first instability, which describe the transition from the stationary to the
time-dependent state, do not seem to play any special role for the dynamo-effect. Open questions
concern the role of this triadic instability as a trigger for the transition to turbulence, the character of
the turbulence itself (is it three-dimensional or quasi-geostrophic) and the very mechanism that
causes the redistribution of the internal angular momentum and/or torque that goes along with the
significant modification of the large scale pattern of the velocity field.

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