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Instabilities and small-scale waves within the Stewartson layers of a thermally driven rotating annulus

Published online by Cambridge University Press:  21 February 2018

Thomas von Larcher Open the ORCID record for Thomas von Larcher [Opens in a new window] ,
Stéphane Viazzo ,
Uwe Harlander ,
Miklos Vincze  and
Anthony Randriamampianina
Thomas von Larcher*
Affiliation:
Institute of Mathematics, Freie Universität Berlin, Arnimallee 9, D-14195 Berlin, Germany
Stéphane Viazzo
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
Uwe Harlander
Affiliation:
Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology Cottbus-Senftenberg, Siemens-Halske-Ring 14, D-03046 Cottbus, Germany
Miklos Vincze
Affiliation:
MTA-ELTE Theoretical Physics Research Group, Budapest, H-1117, Hungary
Anthony Randriamampianina
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

We report on small-scale instabilities in a thermally driven rotating annulus filled with a liquid with moderate Prandtl number. The study is based on direct numerical simulations and an accompanying laboratory experiment. The computations are performed independently with two different flow solvers, that is, first, the non-oscillatory forward-in-time differencing flow solver EULAG and, second, a higher-order finite-difference compact scheme (HOC). Both branches consistently show the occurrence of small-scale patterns at both vertical sidewalls in the Stewartson layers of the annulus. Small-scale flow structures are known to exist at the inner sidewall. In contrast, short-period waves at the outer sidewall have not yet been reported. The physical mechanisms that possibly trigger these patterns are discussed. We also debate whether these small-scale structures are a gravity wave signal.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 380 - 407
Copyright
© 2018 Cambridge University Press 

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von Larcher et al. supplementary movie 1

Thermally driven rotating annulus: time sequence of the Q-criterion (isosurface $Q=10^(-4) s^(-2)$) displayed in the unfolded cylinder. Orientation view in the ($\Phi,z$)-plane and viewpoint from the inner sidewall. The time period of the animation in physical units 106s (corresponding nearly to a quarter of the drift period).

Download von Larcher et al. supplementary movie 1(Video)
Video 7.5 MB

von Larcher et al. supplementary movie 2

Thermally driven rotating annulus: time sequence of the Q-criterion (isosurface $Q=10^(-4) s^(-2)$) displayed in the unfolded cylinder. Orientation view in the ($\Phi,z$)-plane and viewpoint from the outer sidewall. The time period of the animation in physical units 106s (corresponding nearly to a quarter of the drift period).

Download von Larcher et al. supplementary movie 2(Video)
Video 7.6 MB

von Larcher et al. supplementary movie 3

Tracks of particles in the thermally driven rotating annulus: 4 millions of particles released in a ($\phi,r$) plane located at the top of the cavity (in the Ekman boundary layer). Particles are colored by the local temperature. The particles are tracked during 266.5s (the drift period is equal to 380s).

Download von Larcher et al. supplementary movie 3(Video)
Video 11.2 MB

von Larcher et al. supplementary movie 4

Tracks of particles in the thermally driven rotating annulus: 4 millions of particles released in a ($\phi,z$) plane inside the Stewartson inner sidewall boundary layer (at radius $r=45.15 mm$). Particles are colored by the local temperature. The particles are tracked during 266.5s (the drift period is equal to 380s).

Download von Larcher et al. supplementary movie 4(Video)
Video 14.9 MB