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

  • Thomas von Larcher (a1), Stéphane Viazzo (a2), Uwe Harlander (a3), Miklos Vincze (a4) and Anthony Randriamampianina (a2)...
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.

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Corresponding author
Email address for correspondence: larcher@math.fu-berlin.de
References
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Type Description Title
VIDEO
Movies

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).

 Video (11.2 MB)
11.2 MB
VIDEO
Movies

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).

 Video (7.6 MB)
7.6 MB
VIDEO
Movies

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).

 Video (7.5 MB)
7.5 MB
VIDEO
Movies

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).

 Video (14.9 MB)
14.9 MB

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