The kinetic theory of point vortices

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 454, Issue 1970, 1998, Pages 587-606

  Marmanis, Haralambos ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Point vortices; Scaling laws; Statistical dynamics; Two dimensional turbulence; Vortex dynamics

Indexed keywords

EID: 29444458495     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0175     Document Type: Article

References (50)

1. Aref, H. 1979 Motion of three vortices. Phys. Fluids 22, 393-400.
2. Aref, H. 1983 Integrable, chaotic and turbulent vortex motion in two-dimensional flows. A. Rev. Fluid Mech. 15, 345-389.
3. Aref, H. & Eckhardt, B. 1988 Integrable and chaotic motions of four vortices. II. Collision dynamics of vortex pairs. Phil. Trans. R. Soc. Lond. A 326, 655-696.
4. Aref, H. & Siggia, E. D. 1980 Vortex dynamics of the two-dimensional turbulent shear layer. J. Fluid Mech. 100, 705-737.
5. Aref, H. & Siggia, E. D. 1981a Point vortex simulation of the inverse cascade in two-dimensional turbulence. Phys. Fluids 24, 171-172.
6. Aref, H. & Siggia, E. D. 1981b Evolution and breakdown of a vortex street in two dimensions. J. Fluid Mech. 109, 435-463.
7. Aref, H. & Zawadzki, I. 1993 Vortex interactions as a dynamical system. In New approaches and concepts in turbulence (ed. Th. Dracos & A. Tsinober), pp. 191-205. Basel: Birkhauser
8. Babiano, A., Basdevant, C., Legras, B. & Sadourny, R. 1987 Vorticity and passive-scalar dynamics in two-dimensional turbulence. J. Fluid Mech. 183, 379-397.
9. Batchelor, G. K. 1952 The theory of homogeneous turbulence. Cambridge University Press.
10. Batchelor, G. K. 1967 An introduction to fluid dynamics. Cambridge University Press.
11. Benzi, R., Patarnello, S. & Santangelo, P. 1987 On the statistical properties of two-dimensional decaying turbulence. Europhys. Lett. 3, 811-818.
12. Benzi, R., Collela, M., Briscolini, M. & Santangelo, P. 1992 A simple point vortex model for two-dimensional decaying turbulence. Phys. Fluids A 4, 1036-1039.
13. Bogolubov, N. N. 1965 The dynamical theory in statistical physics. International monographs series. Hindustan Publishing Corp. India.
14. Brachet, M. E., Meneguzzi, M., Politano, H. & Sulem, P. L. 1988 The dynamics of freely decaying two-dimensional turbulence. J. Fluid Mech. 194, 333-349.
15. Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775-816.
16. Carnevale, G. F., McWilliams, J. C., Pomeau, Y., Weiss, J. B. & Young, W. R. 1991 Evolution of vortex statistics in two-dimensional turbulence. Phys. Rev. Lett. 66, 2735-2737.
17. Chorin, A. J. 1994 Vorticity and turbulence. New York: Springer.
18. Corrsin, S. 1959 Outline of some topics in homogeneous turbulent flow. J. Geophys. Res. 64, 2134-2150.
19. Couder, Y. 1984 Two-dimensional grid turbulence in a thin liquid film. J. Phys. Lett. 45, 353-360.
20. Couder, Y. & Basdevant, C. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225-251.
21. Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13-31.
22. Gröbli, W. 1877 Specielle probleme über die bewegung geradliniger paralleler wirbelfäden, p. 86. Zürich: Zürcher und Furrer.
23. Helmholtz, H. 1858 On integrals of the hydrodynamical equations which express vortex-motion. Phil. Mag. 33, 485-512 (Engl. transl. Tait, P. G. 1867).
24. Hogg, N. G. & Stommel, H. M. 1985a The heton, an elementary interaction between discrete baroclinic geostrophic vortices and its implications concerning eddy heat-flow. Proc. R. Soc. Lond. A 397, 1-20.
25. Hogg, N. G. & Stommel, H. M. 1985a Hetonic explosions: the breakup and spread of warm pools as explained by baroclinic point vortices. J. Atmos. Sci. 42, 1465-1476.
26. Kida, S. 1975 Statistics of a system of line vortices. J. Phys. Soc. Jap. 39, 1395-1404.
27. Kirchhoff, G. 1883 Vorlesungen über mathematische Physik., Mechanik.
28. Kraichnan, R. H. & Montgomery, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547-619.
29. Lamb, H. 1932 Hydrodynamics. New York: Dover.
30. Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671-673.
31. Lin, C. C. 1943 On the motion of vortices in two dimensions. University of Toronto Press.
32. Lundgren, T. S. 1982 Strained spiral vorex model for turbulent fine structure. Phys. Fluids 25, 2193-2203.
33. McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21-43.
34. Marmanis, H. 1995 Statistical vortex dynamics and two-dimensional turbulence. Masters thesis, University of Illinois at Urbana-Champaign, Urbana.
35. Melander, M. V., Zabusky, N. J. & McWilliams, J. C. 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303-340.
36. Moreau, R. (ed.) 1983 Turbulence bidimensionnelle. J. Méc. Théor. Appl. numéro spécial.
37. Novikov, E. A. & Sedov, Yu. B. 1978 Stochastic properties of a four-vortex system. Sov. Phys. JETP 48, 440-444.
38. Novikov, E. A. 1975 Dynamics and statistics of a system of vortices. Sov. Phys. JETP 41, 937-943.
39. Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cimenta (suppl.) 6, 279-287.
40. Poincaré, H. 1893 Théorie des Tourbillons (ed. G. Carré), p. 211. Paris: Deslis Frères.
41. Résibois, P. & De Leener, M. 1977 Classical kinetic theory of fluids. New York: Wiley.
42. Roberts, P. H. & Donnelly, R. J. 1974 Superfluid mechanics. Ann. Rev. Fluid Mech. 6, 179-225.
43. Saffman, P. G. 1981 Dynamics of vorticity, J. Fluid Mech. 106, 49-58.
44. Saffman, P. G. 1992 Vortex dynamics. Cambridge University Press.
45. Synge, J. L. & Lin, C. C. 1943 On a statistical model of isotropic turbulence. Trans. R. Soc. Canada 37, sec. III, 45-79.
46. Tabeling, P., Burkhart, S., Cardoso, O. & Willaime, H. 1991 Experimental study of freely decaying two-dimensional turbulence. Phys. Rev. Lett. 67, 3772-3775.
47. Tatsuno, M. & Honji, H. 1977 Two pairs of rectilinear vortices. J. Phys. Soc. Japan 42, 361-362.
48. Thompson, P. D. 1957 Uncertainty of initial state as a factor in the predictability of large scales atmospheric flow patterns. Tellus 9, 275-295.
49. Townsend, A. A. 1951 On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A 208, 534-542.
50. Weiss, J. 1981 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. LJI-TN-81-121. La Jolla Institute, La Jolla, California.