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| Titel |
Inertial waves in a spherical shell induced by librations of the inner sphere: experimental and numerical results |
| VerfasserIn |
Sandy Koch, Uwe Harlander, Rainer Hollerbach, Christoph Egbers |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250075925
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| Zusammenfassung |
| In geophysical fluids, such as the atmosphere, the oceans or the liquid core of the earth,
periodic flows can be found on all scales. Due to multiple reflection, e.g. on the curved
boundaries of the spherical shell, wave energy can be focused on certain orbits [1,2],
called wave attractors. These detached internal boundary layers have been studied
experimentally in a rotating box [1], or a rotating cylindrical gap [3] since about 10
years.
We begin with an experimental investigation of the flow induced in a rotating spherical
shell. The shell globally rotates with angular velocity Ω. A further periodic oscillation with
angular velocity 0 -¤ Ïg= 2Ω, a so-called longitudinal libration, is added on the inner
sphere’s rotation. The primary response is an inertial wave spawned at the critical
latitudes on the inner sphere, and propagating throughout the shell along inclined
characteristics. For sufficiently large libration amplitudes the higher harmonics also become
important. Those harmonics whose frequencies are still less than 2Ω behave as
inertial wave themselves, propagating along their own characteristics. The steady
component of the flow consists of a prograde zonal jet on the cylinder tangent to
the inner sphere and parallel to the axis of rotation, and increases with decreasing
Ekman number. The jet becomes unstable for larger forcing amplitudes as can be
deduced from preliminary particle image velocimetry observations. Finally, a wave
attractor is experimentally detected in the spherical shell as the pattern of largest
variance.
These findings are reproduced in a 2D numerical investigation of the flow, and certain
aspects can be studied numerically in greater detail. One aspect is the scaling of the width of
the inertial shear layers and the width of the steady jet. Another is the partition of the kinetic
energy between the forced wave, its harmonics, and the mean flow. Finally, the numerical
simulations allow for an investigation of instabilities, too local to be found experimentally.
For strong libration amplitudes the boundary layer on the inner sphere becomes
unstable, triggering localised Görtler vortices during the prograde phase of the forcing.
This instability is important for the transition to turbulence of the spherical shell
flow.
References
[1] L.R.M. Maas, J. Fluid Mech. 437, 13-28, 2001
[2] U. Harlander and L.R.M.Maas, Dynamics of Atmospheres and Oceans 44, 1-28,
2007
[3] Swart, A. and Manders, A. and Harlander, U. and Maas, L.R.M., Dynamics of
Atmospheres and Oceans, Vol. 50, 16-34, 2010 |
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