Drehimpulstransport in einem geschichteten Taylor-Couette Experiment mit Anwendungen auf Akkretionsscheiben
Zusammenfassung der Projektergebnisse
Stratified rotating flows play a central role in the Geosciences and they have many applications in Meteorology, Oceanography, Planetary Sciences and Astrophysics. Superficially, one would expect that stratification makes rotating flows more stable. However, stratification renders wave motions possible that are not existing in purely rotating flows. These are inertial gravity waves that in fact are ubiquitous in geophysical flows. Such waves may interact leading to new and unexpected instabilities. A longstanding issue in astrophysical flows is to properly explain the outward momentum transport in accretion disks. Such disks, when considered as non-stratified objects, are hydrodynamically stable which excludes the existence of turbulence. However, the latter is needed to explain the outward momentum flux. One possibility to overcome this problem is to consider the disk as stratified. In that case inertia gravity modes can interact in a way that destabilizes the flow in the disk. In the project we studied this stratorotational instability (SRI) experimentally. The experiment consists of a thermally stratified Taylor-Couette system. The axial stratification is due to cooling at the bottom and heating at the top. With this system we experimentally investigated under which conditions we can expect SRI and we further studied the spatio-temporal structure of the SRI modes, their propagation characteristics and the momentum transport related to the unstable modes. The SRI experiment performed at the BTU Cottbus-Senftenberg is the first one that actually uses heating and cooling for the stratification and not salt. Salt stratified systems have the disadvantage that mixing leads to an irreversible destruction of the stratification whereas thermal stratified systems can recover the stratification due to the imposed boundary conditions. We found a surprisingly complex structure of the domain of instability in the space spanned by the Reynolds number and the rotation ratio of the inner and outer cylinder. The structure deviates strongly from the one that has been proposed from a low-Reynolds number salt-stratified system. Later is could be shown that for somewhat larger Reynolds numbers the results from the salt- and temperature-stratified experiments agree fairly well. We further proved by linear stability analysis that the complexity of the instability diagram is not due to nonlinear effects but can be explained completely by linear theory. By using Particle Image Velocimetry (PIV) we could clearly show that SRI is due to a resonance between boundary trapped inertia gravity waves. This idea was proposed earlier on the basis of numerical simulations. The modes propagate almost without dispersion that corresponds well with findings from theoretical models. By computing the Reynolds stress terms from horizontal PIV data we could show that the momentum transport is generally outward implying that SRI is a candidate for explaining momentum loss in accretion disks without magnetic fields. The momentum flux is large in the center of the SRI region and rapidly drops when the boundaries for instability are reached. Outside the SRI region the flow is rather stable even for large Reynolds numbers (up to 2500). We found signs for Ekman layer instability with a mode structure that might be confused with SRI modes. Open issue is whether the SRI modes itself could become unstable, maybe interacting in the form of resonant triads leading to a collapse of the rather laminar SRI flow. However, this is the subject of an ongoing project in the frame of a binational French-German Cotutelle program where we combine the experiment with high-performance computing to get more insight into the high Reynolds number state.
Projektbezogene Publikationen (Auswahl)
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2015 Stratorotational instability in a thermally stratified Taylor-Couette Flow. European Geosciences Union (EGU) General Assembly 2015, held 12.-17. April 2015, Vienna Austria
Harlander, U., Seelig, T., Gellert, M., Viazzo, S., Randriamampianina, A., Egbers, Ch., Rüdiger, G.
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2015 Stratorotational Instability: nonlinear aspects at higher Reynolds numbers 19th International Couette-Taylor Workshop, 24-26 June 2015, Cottbus, Germany
Harlander, U., Seelig, T., Stapelfeld, L., Gellert, M., Viazzo, S., Randriamampianina, A., Egbers, Ch., Rüdiger, G.
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2015 Stratorotational instability: nonlinear aspects at higher Reynolds numbers, EUROMECH Colloquium 567 - Turbulent mixing in stratified flows, 22.-25. March 2015, Cambridge, UK
Harlander, U., Seelig, T., Gellert, M., Viazzo, S., Randriamampianina, A., Egbers, Ch., Rüdiger, G.
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PIV measurements in an axially stratified Taylor-Couette experiment GALA - Fachtagung Experimentelle Strömungsmechanik, 6-8.09.2016, Cottbus, ISBN 978-3-9816764-2-6
Seelig, T., Burchardt, M., Krebs, A., Harlander, U., Egbers, Ch.
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PIV measurements in an axially stratified Taylor-Couette experiment School ISTROF 2016, Instabilities and Turbulence in Strato-Rotational Flows, July 11-13th, 2016, Le Havre
Seelig, T., Burchardt, M., Krebs, A., Harlander, U., Egbers, Ch.
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The stratorotational instability of Taylor-Couette flows of moderate Reynolds numbers. Geophysical and Astrophysical Fluid Dynamics, 111, 429–447, 2017
G. Rüdiger, T. Seelig, M. Schultz, M. Gellert, C. Egbers, U. Harlander
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Experimental investigation of stratorotational instability using a thermally stratified system: instability, waves and associated momentum flux. Geophys. Astrophys. Fluid Dyn., 112, 239-264, 2018
T. Seelig, U. Harlander, M. Gellert
