Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-19T16:00:35.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Stratorotational instability in Taylor–Couette flow heated from above

Published online by Cambridge University Press:  06 March 2009

M. GELLERT  and
G. RÜDIGER
M. GELLERT*
Affiliation:
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
G. RÜDIGER
Affiliation:
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the instability and nonlinear saturation of temperature-stratified Taylor–Couette flows in a finite height cylindrical gap and calculate angular momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients, the differential rotation as well as the stratification due to the temperature gradient, are stable themselves, together the system becomes subject of the stratorotational instability and a non-axisymmetric flow pattern evolves. This flow configuration transports angular momentum outwards and will therefore be relevant for astrophysical applications. The belonging coefficient of β viscosity is of the order of unity if the results are adapted to the size of an accretion disk. The strength of the stratification, the fluid's Prandtl number and the boundary conditions applied in the simulations are well suited too for a laboratory experiment using water and a small temperature gradient around 5 K. With such a set-up the stratorotational instability and its angular momentum transport could be measured in an experiment.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 375 - 385
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balbus, S. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I – Linear analysis; II – Nonlinear evolution. Astrophys. J. 376, 214–233.CrossRefGoogle Scholar
Boubnov, B. M., Gledzer, E. B. & Hopfinger, E. J. 1995 Stratified circular Couette flow: instability and flow regime. J. Fluid Mech. 292, 333–358.CrossRefGoogle Scholar
Boubnov, B. M., Gledzer, E. B., Hopfinger, E. J. & Orlandi, P. 1996 Layer formation and transitions in stratified circular Couette flow. Dyn. Atmos. Oceans 23, 139–153.CrossRefGoogle Scholar
Caton, F., Janiaud, B. & Hopfinger, E. J. 2000 Stability and bifurcations in stratified Taylor–Couette flow. J. Fluid Mech. 419, 93–124.CrossRefGoogle Scholar
Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High Order Methods for Incompressible Fluid Flow. Cambridge University Press.CrossRefGoogle Scholar
Dubrulle, B., Marié, L., Normand, Ch., Richard, D., Hersant, F. & Zahn, J. P. 2005 A hydrodynamic shear instability in stratified disks. Astron. Astrophys. 429, 1–13.CrossRefGoogle Scholar
Fournier, A., Bunge, H.-P., Hollerbach, R. & Vilotte, J.-P. 2005 A Fourier-spectral element algorithm for thermal convection in rotating axisymmetric containers. J. Comput. Phys. 204, 462–489.CrossRefGoogle Scholar
Gellert, M. & Rüdiger, G. 2008 Toroidal field instability and eddy viscosity in Taylor–Couette flows. Astron. Nachr. 329, 709–713.CrossRefGoogle Scholar
Gellert, M., Rüdiger, G. & Fournier, A. 2007 Energy distribution in nonaxisymmetric magnetic Taylor–Couette flow. Astron. Nachr. 328, 1162–1165.CrossRefGoogle Scholar
Huré, J.-M., Richard, D. & Zahn, J.-P. 2001 Accretion discs models with the β-viscosity prescription derived from laboratory experiments. Astron. Astrophys. 367, 1087–1094.CrossRefGoogle Scholar
Le Bars, M. & Le Gal, P. 2006 Experimental analysis of the stratorotational instability in a cylindrical Couette flow. Phys. Rev. Lett. 99, id. 064502.Google Scholar
Lynden-Bell, D. & Pringle, J. E. 1974 The evolution of viscous discs and the origin of the nebular variables. Mon. Not. R. Astron. Soc. 168, 603–637.CrossRefGoogle Scholar
Molemaker, M. J., McWilliams, J. C. & Yavneh, I. 2001 Instability and equilibration of centrifugally stable stratified Taylor–Couette flow. Phys. Rev. Lett. 86, 5270–5273.CrossRefGoogle ScholarPubMed
Rüdiger, G., Hollerbach, R., Schultz, M. & Elstner, D. 2007 Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields. Mon. Not. R. Astron. Soc. 377, 1481–1487.CrossRefGoogle Scholar
Rüdiger, G., & Shalybkov, D. 2008 Stratorotational instability in MHD Taylor–Couette flows. Astron. Astrophys., accepted, arXiv: 0808.0577v1.Google Scholar
Shalybkov, D. & Rüdiger, G. 2005 Stability of density-stratified viscous Taylor–Couette flows. Astron. Astrophys. 438, 411–417.CrossRefGoogle Scholar
Shakura, N. I., & Sunyaev, R. A. 1973 Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355.Google Scholar
Tayler, R. J. 1957 Hydromagnetic instabilities of an ideally conducting fluid. Proc. Phys. Soc. B 70, 31–48.CrossRefGoogle Scholar
Thorpe, S. A. 1968 A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 693–704.CrossRefGoogle Scholar
Umurhan, O. M. 2006 On the stratorotational instability in the quasi-hydrostatic semi-geostrophic limit. Mon. Not. R. Astron. Soc. 365, 85–100.CrossRefGoogle Scholar
Withjack, E. M. & Chen, C. F. 1974 An experimental study of Couette instability of stratified fluids. J. Fluid Mech. 66, 725–737.CrossRefGoogle Scholar
Yavneh, I., McWilliams, J. C. & Molemaker, M. J. 2001 Non-axisymmetric instability of centrifugally stable stratified Taylor–Couette flow. J. Fluid Mech. 448, 1–21.CrossRefGoogle Scholar