Abstract
We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small tilt angles the vortices tend to align along the cylinder axis and not along the rotation axis. We also show that the axial flow along the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson instability above some critical tilt angle. When the vortices become unstable the final state often appears to be a dynamical steady state, which may contain turbulent regions where new vortices are constantly created. These new vortices push other vortices in regions with laminar flow towards the top and bottom ends of the cylinder where they finally annihilate. Experimentally the inclined cylinder could be a convenient environment to create long lasting turbulence with a polarization which can be adjusted with the tilt angle.
Similar content being viewed by others
References
D. Stauffer, A.L. Fetter, Phys. Rev. 168, 156 (1968)
J.A. Northby, R.J. Donnelly, Phys. Rev. Lett. 25, 214 (1970)
V.M. Ruutu, J.J. Ruohio, M. Krusius, B. Plaçais, E.B. Sonin, Physica B 255, 27 (1998)
A.P. Finne, V.B. Eltsov, G. Eska, R. Hänninen, J. Kopu, M. Krusius, E.V. Thuneberg, M. Tsubota, Phys. Rev. Lett. 96, 085301 (2006)
P. Mathieu, B. Plaçais, Y. Simon, Phys. Rev. B 29, 2489 (1984)
M. Kobayashi, M. Tsubota, Phys. Rev. A 76, 045603 (2007)
M. Kobayashi, M. Tsubota, J. Low Temp. Phys. 150, 587 (2008)
L.M. Milne-Thomson, Theoretical Hydrodynamics, 5th edn. (Macmillan, New York, 1968)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1963)
V.B. Eltsov, R. de Graaf, R. Hänninen, M. Krusius, R.E. Solntsev, V.S. L’vov, A.I. Golov, P.M. Walmsley, in Progress in Low Temperature Physics: Quantum Turbulence, vol. 16 (2009), pp. 45–146
V.M.H. Ruutu, Ü. Parts, J.H. Koivuniemi, N.B. Kopnin, M. Krusius, J. Low Temp. Phys. 107, 93 (1997)
K.W. Schwarz, Phys. Rev. B 31, 5782 (1985)
K.W. Schwarz, Phys. Rev. B 38, 2398 (1988)
T.D.C. Bevan, A.J. Manninen, J.B. Cook, H. Alles, J.R. Hook, H.E. Hall, J. Low Temp. Phys. 109, 423 (1997)
T.D.C. Bevan, A.J. Manninen, J.B. Cook, A.J. Armstrong, J.R. Hook, H.E. Hall, Phys. Rev. Lett. 74, 750 (1995)
E.B. Sonin, Rev. Mod. Phys. 59, 87 (1987)
A.P. Finne, T. Araki, R. Blaauwgeers, V.B. Eltsov, N.B. Kopnin, M. Krusius, L. Skrbek, M. Tsubota, G.E. Volovik, Nature 424, 1022 (2003)
M. Tsubota, C.F. Barenghi, T. Araki, A. Mitani, Phys. Rev. B 69, 134515 (2004)
M. Tsubota, T. Araki, C.F. Barenghi, Phys. Rev. Lett. 90, 205301 (2003)
V.B. Eltsov, A.P. Finne, R. Hänninen, J. Kopu, M. Krusius, M. Tsubota, E.V. Thuneberg, Phys. Rev. Lett. 96, 215302 (2006)
R.J. Zieve, L.A.K. Donev, J. Low Temp. Phys. 121, 199 (2000)
R. Hänninen, A. Mitani, M. Tsubota, J. Low Temp. Phys. 138, 589 (2005)
V.B. Eltsov, A.I. Golov, R. de Graaf, R. Hänninen, M. Krusius, V.S. L’vov, R.E. Solntsev, Phys. Rev. Lett. 99, 265301 (2007)
W.I. Glaberson, W.W. Johnson, R.M. Ostermeier, Phys. Rev. Lett. 33, 1197 (1974)
R.M. Ostermeier, W.I. Glaberson, J. Low Temp. Phys. 21, 191 (1975)
R.J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hänninen, R. Rotating Inclined Cylinder and the Effect of the Tilt Angle on Vortices. J Low Temp Phys 156, 145–162 (2009). https://doi.org/10.1007/s10909-009-9897-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-009-9897-8