Abstract
Two-dimensional flows with high Reynolds numbers have the striking property of organizing spontaneously into coherent structures. The robustness of Jupiter’s Great Red Spot, a huge vortex persisting for more than three centuries in a turbulent shear between two zonal jets, is probably related to this general phenomenon. Similarly, it is striking to observe that galaxies themselves follow a kind of organization revealed in the Hubble classification or in de Vaucouleur’s R 1/4 law for the surface brightness of ellipticals (Binney & Tremaine, 1987). We shall discuss some analogies between stellar systems and 2D vortices and show that their structure and organization can be understood from relatively similar statistical mechanics [for a short review on this subject see Chavanis (1998a)].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Binney, J. and Tremaine, S. (1987) Galactic Dynamics (Princeton Series in Astrophysics)
Chandrasekhar, S. (1943) Principles of stellar dynamics (Dover)
Chavanis, P.H. (1998a) From Jupiter’s Great Red Spot to the structure of galaxies: statistical mechanics of two-dimensional vortices and stellar systems, Annals of the New York Academy of Sciences,Vol. 867, pp. 120–141
Chavanis, P.H. (1998b) On the coarse-grained evolution of collisionless stellar systems, Mon. Not. R. Astr. Soc., Vol. 300, pp. 981–991
Chavanis, P.H. (1998c) Systematic drift experienced by a point vortex in two-dimensional turbulence, Phys. Rev. E,Vol. 58, pp. R1199–R1202
Chavanis, P.H. and Sommeria, J. (1996) Classification of self-organized vortices in two-dimensional turbulence: the case of a bounded domain, J. Fluid Mech.,Vol. 314, pp. 267–297
Chavanis, P.H. and Sommeria, J. (1998a) Degenerate equilibrium states of collisionless stellar systems, Mon. Not. R. Astr. Soc., Vol. 296, pp. 569–578
Chavanis, P.H. and Sommeria, J. (1998b) Classification of robust isolated vortices in two-dimensional hydrodynamics, J. Fluid Mech.,Vol. 356, pp. 259–296
Chavanis, P.H., Sommeria, J. and Robert, R. (1996) Statistical mechanics of two-dimensional vortices and collisionless stellar systems, Astrophys. J.,Vol. 471, pp. 385–399
Joyce, G. and Montgomery, D. (1973) Negative temperature states for the two-dimensional guiding-center plasma, J. Plasma Physics,Vol. 10, pp. 107–121
Lynden-Bell, D. (1967) Statistical mechanics of violent relaxation in stellar systems, Mon.Not. R. Astr. Soc.,Vol. 136, pp. 101–121
Miller, J. (1990) Statistical mechanics of the Euler equation in two dimensions, Phys. Rev. Lett., Vol. 65, pp. 2137–2140
Onsager, L. (1949) Statistical hydrodynamics, Nuovo Cimento Suppl.,Vol. 6, pp. 279–287
Robert, R. and Rosier, C. (1997) The modelling of small scales in two-dimensional turbulent flows: a statistical mechanics approach, J. Stat. Phys., Vol. 86, pp. 481–515
Robert, R. and Sommeria, J. (1991) Statistical equilibrium states for two-dimensional flows, J. Fluid Mech., Vol. 229, pp. 291:310
Robert, R. and Sommeria, J. (1992) Relaxation towards a statistical equilibrium state in two-dimensional perfect fluid dynamics, Phys. Rev. Lett., Vol. 69, pp. 2776–2779
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Chavanis, P.H. (2001). On the Analogy between Two-Dimensional Vorticesand Stellar Systems. In: Kambe, T., Nakano, T., Miyauchi, T. (eds) IUTAM Symposium on Geometry and Statistics of Turbulence. Fluid Mechanics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9638-1_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-9638-1_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5614-6
Online ISBN: 978-94-015-9638-1
eBook Packages: Springer Book Archive