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| Titel |
Inertial modes and their transition to turbulence in a differentially rotating spherical gap flow |
| VerfasserIn |
Michael Hoff, Uwe Harlander, Santiago Andres Triana, Christoph Egbers |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250127151
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| Publikation (Nr.) |
 EGU/EGU2016-6990.pdf |
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| Zusammenfassung |
| We present a study of inertial modes in a spherical shell experiment. Inertial modes are
Coriolis-restored linear wave modes, often arise in rapidly-rotating fluids (e.g. in the
Earth’s liquid outer core [1]). Recent experimental works showed that inertial modes
exist in differentially rotating spherical shells. A set of particular inertial modes,
characterized by (l,m,ˆω), where l, m is the polar and azimuthal wavenumber and
ˆω = ω∕Ωout the dimensionless frequency [2], has been found. It is known that they
arise due to eruptions in the Ekman boundary layer of the outer shell. But it is an
open issue why only a few modes develop and how they get enhanced. Kelley et al.
2010 [3] showed that some modes draw their energy from detached shear layers
(e.g. Stewartson layers) via over-reflection. Additionally, Rieutord et al. (2012) [4]
found critical layers within the shear layers below which most of the modes cannot
exist.
In contrast to other spherical shell experiments, we have a full optical access to
the flow. Therefore, we present an experimental study of inertial modes, based on
Particle-Image-Velocimetry (PIV) data, in a differentially rotating spherical gap flow where
the inner sphere is subrotating or counter-rotating at Ωin with respect to the outer spherical
shell at Ωout, characterized by the Rossby number Ro = (Ωin − Ωout)∕Ωout. The radius
ratio of η = 1∕3, with rin = 40mm and rout = 120mm, is close to that of the Earth’s core.
Our apparatus is running at Ekman numbers (E ≈ 10−5, with E = ν∕(Ωoutrout2), two
orders of magnitude higher than most of the other experiments. Based on a frequency-Rossby
number spectrogram, we can partly confirm previous considerations with respect to the onset
of inertial modes. In contrast, the behavior of the modes in the counter-rotation regime is
different. We found a triad interaction between three dominant inertial modes, where one is a
slow axisymmetric Rossby mode [5]. We show that the amplitude of the most dominant mode
(l,m,ˆω) = (3,2,∼ 0.71) is increasing with increasing |Ro| until a critical Rossby
number Rocrit. Accompanying with this is an increase of the zonal mean flow
outside the tangent cylinder, leading to enhanced angular momentum transport. At the
particular Rocrit, the wave mode, and the entire flow, breaks up into smaller-scale
turbulence [6], together with a strong increase of the zonal mean flow inside the
tangent cylinder. We found that the critical Rossby number scales approximately with
E1∕5.
References
[1] Aldridge, K. D.; Lumb, L. I. (1987): Inertial waves identified in the Earth’s
fluid outer core. Nature 325 (6103), S. 421–423. DOI: 10.1038/325421a0.
[2] Greenspan, H. P. (1968): The theory of rotating fluids. London: Cambridge U.P.
(Cambridge monographs on mechanics and applied mathematics).
[3] Kelley, D. H.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2010):
Selection of inertial modes in spherical Couette flow. Phys. Rev. E 81 (2), 26311.
DOI: 10.1103/PhysRevE.81.026311.
[4] Rieutord, M.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2012):
Excitation of inertial modes in an experimental spherical Couette flow. Phys. Rev. E
86 (2), 026304. DOI: 10.1103/PhysRevE.86.026304.
[5] Hoff, M., Harlander, U., Egbers, C. (2016): Experimental survey of linear and
nonlinear inertial waves and wave instabilities in a spherical shell. J. Fluid Mech.,
(in print)
[6] Kerswell, R. R. (1999): Secondary instabilities in rapidly rotating fluids:
inertial wave breakdown. Journal of Fluid Mechanics 382, S. 283–306. DOI:
10.1017/S0022112098003954. |
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