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| Titel |
Mean flow generation in a rotating straight and sloping wall annulus with librating walls |
| VerfasserIn |
Abouzar Ghasemi V., Marten Klein, Torsten Seelig, Uwe Harlander, Eberhard Schaller, Andreas Will |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250099356
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| Publikation (Nr.) |
 EGU/EGU2014-15126.pdf |
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| Zusammenfassung |
| The work presented is about the investigation of the mean flow generation mechanism
in a rotating straight and sloping wall annulus with librating walls. Three mean
flow generation mechanism may be identified: the mean flow driven by inertial
wave-wave interaction, mean flow driven by the action of Reynolds stress and mean
flow driven by friction. Direct numerical simulation together with a laboratory
experiment is used to investigate it. An incompressible Navier-Stokes solver with the
equations formulated for volume fluxes in generalized curvilinear coordinates has been
used. In terms of geometry, the current investigation is divided into two parts: mean
flow generation mechanism in (i) a sloping wall annulus and (ii) a straight wall
annulus.
For the sloping wall annulus we investigated mean flow induced by inertial wave-wave
interaction and friction. Under consecutive reflections in a sloping wall annulus inertial
waves may form wave attractors. It will be shown that when boundary layer over
the sloping wall is centrifugally stable, a retrograde mean flow may be generated
due to the focusing of inertial wave beam from the sloping wall via the inertial
wave-wave interaction. In addition, we observed a prograde mean flow which is
induced by the effect of friction and is scaled as a Stewartson layer. We studied the
appearance of this mean flow by librating top/bottom lids and sloping wall either
independently or together. A comparison with laboratory experiment (PIV) will be
shown.
In the second part, mean flow in a straight wall annulus induced by the effect of Reynolds
stress and friction is investigated. To study mean flow generation mechanism, we allow
top/bottom lids and inner and outer cylinder side walls librate either together or
independently. It has been shown experimentally (Noir et al. 2010) that a retrograde mean
flow in the bulk of the fluid is due to the nonlinearity of the Ekman boundary layer
and instability of the Stokes boundary layer and inertial waves does not have any
contribution to that. In contrast, by libration of top/bottom lids and cylinder side
walls independently or together we showed that the contribution of the unstable
Stokes boundary layer and inertial waves is not negligible. By making an analogy to
the acoustic standing waves, it will be explained that inertial waves may modify
the bulk mean flow by the formation of standing wave via the action of Reynolds
Stress. According to Ekman number, libration amplitude and libration frequency,
Stokes boundary layer may be centrifugally stable or unstable. Unstable stokes
boundary layer generates Geortler vortices. These vortices diffuse away into the
bulk and via the effect of Reynolds stress generates a mean flow (called steady
streaming). This mean flow is retrograde and prograde close to the outer and inner
cylinder side wall, respectively. It is observed that the libration of tops/bottom lids
together with cylinder side walls reduces the amplitude of the Steady streaming
when Stokes boundary layer is centrifugally unstable and increases the amplitude
of the Stewartson layer when Stokes boundary layer is centrifugally stable. By
considering Reynolds average equations as diagnostic equations, the generation
mechanism and the sign selection of the steady streaming will be discussed. It will be
shown that steady streaming is a result of inverse cascade of energy from turbulent
fluctuations to the mean flow. A comparison with laboratory experiment (PIV) will be
shown.
Acknowledgement
This work is a part of the project "Mischung und Grundstromanregung durch
propagierende Trgheitswellen: Theorie, Experiment und Simulation", financedby the German
Science Foundation (DFG).
Reference
J. Noir, M. A. Calkins, J. Cantwell and J. M. Aurnou, Experimental study of
libration-driven zonal flows in a straight cylinder. Phys. Earth Planet. Inter. 182 (2010),
98-106. |
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