The breakdown of Alfvén's theorem in ideal plasma flows: Necessary conditions and physical conjectures

Physica D: Nonlinear Phenomena

Volumn 223, Issue 1, 2006, Pages 82-92

  Eyink, Gregory L ^a,b   Aluie, Hussein ^a,b  

^a Johns Hopkins University   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Ideal magnetohydrodynamics; Line motion; Reconnection; Singularities

Indexed keywords

COMPUTER SIMULATION; CONSTRAINT THEORY; ENERGY DISSIPATION; MAGNETIC FLUX; NONLINEAR EQUATIONS; PLASMA FLOW; THEOREM PROVING;

IDEAL MAGNETOHYDRODYNAMICS; LINE MOTION; RECONNECTION;

MAGNETOHYDRODYNAMICS;

EID: 33750161709     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.08.009     Document Type: Article

References (96)

1. Alfvén H. On the existence of electromagnetic-hydrodynamic waves. Ark. Mat., Astron. o. Fys. 29B (1942) 1-7
2. Stern D.P. The motion of magnetic field lines. Space Sci. Rev. 6 (1966) 147-173
3. Helmholtz H. Über Integrale der hydrodynamischen Gleichungen welche den Wirbelbewegungen entsprechen. Crelles J. 55 (1858) 25-55
4. Axford W.I. Magnetic field reconnection. Magnetic Reconnection in Space and Laboratory Plasmas, in: Proceedings of the Chapman Conference on Magnetic Reconnection. 3-7 October, 1983, Los Alamos, NM (1984), American Geophysical Union, Washington, DC 1-8
5. Lazarian A. Astrophysical implications of turbulent reconnection: from cosmic rays to star formation. Magnetic Fields in the Universe: From Laboratory and Stars to Primordial Structures. AIP Conf. Proc. 784 (2005) 42-53
6. Deam R.T., and Edwards S.F. The theory of rubber elasticity. Philos. Trans. R. Soc. Lond. A 280 (1976) 317-353
7. Goldbart P.M., and Goldenfeld N. Sam Edwards and the statistical mechanics of rubber. Stealing the Gold: A Celebration of the Pioneering Physics of Sam Edwards (2004), Clarendon Press, Oxford 275-297
8. Biskamp D. Magnetic Reconnection in Plasmas (2000), Cambridge University Press, Cambridge
9. Priest E., and Forbes T. Magnetic Reconnection: MHD Theory and Applications (2000), Cambridge University Press, Cambridge
10. Parker E.N. Fast dynamos, cosmic rays, and the galactic magnetic fields. Astrophys. J. 401 (1992) 135-145
11. Dere K.P. The rate of magnetic reconnection observed in the solar atmosphere. Astrophys. J. 472 (1996) 864-873
12. Lazarian A., and Vishniac E. Reconnection in a weakly stochastic field. Astrophys. J. 517 (1999) 700-718
13. Lazarian A., and Vishniac E. Fast reconnection of magnetic fields in turbulent fluids. Rev. Mex. Astron. Astrofis. Ser. Conf. 9 (2000) 55-62. astro-ph/0002067
14. Dryden H.L. A review of the statistical theory of turbulence. Q. Appl. Math. 1 (1943) 7-42
15. Sreenivasan K.R. On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27 (1984) 1048-1051
16. Cadot O., Couder Y., Daerr A., Douady S., and Tsinober A. Energy injection in closed turbulent flows: Stirring through boundary layers versus inertial stirring. Phys. Rev. E 56 (1997) 427-433
17. Pearson R.B., Krogstad P.-Å., and van den Water W. Measurements of the turbulent energy dissipation rate. Phys. Fluids 14 (2002) 1288-1290
18. Sreenivasan K.R. An update on the energy dissipation rate in isotropic turbulence. Phys. Fluids 10 (1998) 528-529
19. Kaneda Y., Ishihara T., Yokokawa M., Itakura K., and Uno A. Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15 (2003) L21-L24
20. Onsager L. Statistical hydrodynamics. Nuovo Cimento 6 (1949) 279-287
21. Eyink G.L. Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer. Physica D 78 (1994) 222-240
22. Constantin P., Titi E.S., and E W. Onsager's conjecture on the energy conservation for solutions of the Euler's equations. Comm. Math. Phys. 165 (1994) 207-209
23. Duchon J., and Robert R. Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations. Nonlinearity 13 (2000) 249-255
24. Eyink G.L., and Sreenivasan K.R. Onsager and the theory of hydrodynamic turbulence. Rev. Modern Phys. 78 (2006) 87-136
25. Muzy J.F., Bacry E., and Arneodo A. Wavelets and multifractal formalism for singular signals: Application to turbulence data. Phys. Rev. Lett. 67 (1991) 3515-3518
26. Arneodo A., Bacry E., and Muzy J.F. The thermodynamics of fractals revisited with wavelets. Physica A 213 (1995) 232-275
27. Kestener P., and Arneodo A. Generalizing the wavelet-based multifractal formalism to random vector fields: application to three-dimensional turbulence velocity and vorticity data. Phys. Rev. Lett. 93 (2004) 044501
28. Eyink G.L. Turbulent cascade of circulations. C. R. Phys. 7 (2006) 449-455. physics/0605014
29. G.L. Eyink, Cascade of circulations in fluid turbulence, Phys. Rev. E (2006) (submitted for publication). physics/0606159
30. S. Chen, G.L. Eyink, M. Wan, Z. Xiao, Is the Kelvin theorem valid for high-Reynolds-number turbulence? Phys. Rev. Lett. (2006) (in press). physics/0605016
31. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability (1961), Oxford University Press, Oxford
32. Zorawski K. Über die Erhaltung der Wirbelbewegung. Bull. Acad. Sci. Cracovie, C. R. (1900) 335-342
33. Abraham R., Marsden J.E., and Ratiu T. Manifolds, Tensor Analysis, and Applications. Applied Mathematical Sciences vol. 75 (1983), Springer-Verlag, Berlin 370 pp
34. Ruban V.P. Motion of magnetic flux lines in magnetohydrodynamics. J. Exp. Theor. Phys. 89 (1999) 299-310
35. Schindler K., Hesse M., and Birn J. General magnetic reconnection, parallel electric fields, and helicity. J. Geophys. Res. 93 (1988) 5547-5557
36. Hesse M., and Schindler K. A theoretical foundation of general magnetic reconnection. J. Geophys. Res. 93 (1988) 5559-5567
37. Schindler K. Kinematics of magnetic reconnection in three dimensions. Physics of the Magnetopause. Geophysical Monograph vol. 90 (1995), American Geophysical Union, Washington, DC 197-204
38. Friedlander F.G. Introduction to the Theory of Distributions. 2nd ed. (1998), Cambridge University Press, Cambridge
39. Hörmander L. The Analysis of Linear Partial Differential Operators vol. 3 (1985), Springer-Verlag, Berlin
40. Steenbeck M., Krause F., and Rädler K.-H. Berechnungen der mittleren Lorentz Feldstärke für ein elektrisch leitendes Medium in turbulenter. Z. Naturf. A 21 (1966) 369-376 translated in NCAR-TN/IA-60, The turbulent dynamo, edited by P. H. Roberts, M. Stix, 1971, p. 29
41. Moffatt H.K. The mean electromotive force generated by turbulence in the limit of perfect conductivity. J. Fluid Mech. 65 (1974) 1-10
42. Krause F., and Rädler K.-H. Mean Field Magnetohydrodyamics and Dynamo Theory (1980), Akademie-Verlag, Berlin
43. Goldenfeld N.D. Lectures on Phase Transitions and the Renormalization Group. Frontiers in Physics vol. 85 (1992), Addison-Wesley, Reading, MA
44. Moffatt H.K. Transport effects associated with turbulence with particular attention to the influence of helicity. Rep. Prog. Phys. 46 (1983) 621-664
45. Wilson K.G. Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Phys. Rev. B 4 (1971) 3174-3183
46. Wilson K.G. Renormalization group and critical phenomena. II. phase-space cell analysis of critical behaviour. Phys. Rev. B 4 (1971) 3184-3205
47. Wilson K.G. The renormalization group: Critical phenomena and the Kondo problem. Rev. Modern Phys. 47 (1975) 773-840
48. Germano M. Turbulence - the filtering approach. J. Fluid Mech. 238 (1992) 325-336
49. Meneveau C., and Katz J. Scale-invariance and turbulence models for large-eddy-simulation. Ann. Rev. Fluid Mech. 32 (2000) 1-32
50. Newcomb W.A. Motion of magnetic lines of force. Ann. Phys. NY 3 (1958) 347-385
51. Boozer A.H. The evolution of magnetic fields and plasmas in open field line configurations. Phys. Fluids B 2 (1990) 2300-2305
52. Mestel L., and Spitzer L. Star formation in magnetic dust clouds. Mon. Not. R. Astron. Soc. 116 (1956) 503-514
53. Tassis K., and Mouschovias T.C. Ambipolar-diffusion timescale, star formation timescale, and the ages of molecular clouds: is there a discrepancy?. Astrophys. J. 616 (2004) 283-287
54. Braginskii S.I. Transport processes in a plasma. Rev. Plasma Phys. 1 (1965) 205-310
55. Schekochihin A.A., Cowley C.S., Kulsrud R.M., Hammett G.W., and Sharma P. Plasma instabilities and magnetic-field growth in clusters of galaxies. Astrophys. J. 629 (2005) 139-142
56. Ilin K.I., Trakhinin Y.L., and Vladimirov V.A. The stability of steady magnetohydrodynamic flows with current-vortex sheets. Phys. Plasmas 10 (2003) 2649-2658
57. Landau L.D., and Lifshitz E.M. Electrodynamics of Continuous Media. Course of Theoretical Physics vol. 8 (1960), Pergamon Press, Oxford
58. Frisch U., Pouquet A., Sulem P.L., and Meneguzzi M. The dynamics of two-dimensional ideal MHD. J. Méc. Théor. Appl. numéro spécial (1983) 191-216
59. Biskamp D., and Welter H. Dynamics of decaying two-dimensional magnetohydrodynamic turbulence. Phys. Fluids B 1 (1989) 1964-1979
60. Grauer R., and Marliani C. Geometry of singular structures in magnetohydrodynamic flows. Phys. Plasmas 5 (1998) 2544-2552
61. Sulem P.L., Frisch U., Pouquet A., and Meneguzzi M. On the exponential flattening of current sheets near neutral X-points in two-dimensional ideal MHD flow. J. Plasma Phys. 33 (1985) 191-198
62. Politano H., Pouquet A., and Sulem P.L. Current and vorticity dynamics in three-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 2 (1995) 2931-2939
63. Grauer R., and Marliani C. Current-sheet formation in 3D ideal incompressible magnetohydrodynamics. Phys. Rev. Lett. 84 (2000) 4850-4853
64. Maron J., and Goldreich P. Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554 (2001) 1175-1196
65. Langer J.S., and Ambegaokar V. Intrinsic resistive transition in narrow superconducting channels. Phys. Rev. 164 (1967) 498-510
66. McCumber D.E., and Halperin B.I. Time scale of intrinsic resistive fluctuations in thin superconducting wires. Phys. Rev. B 1 (1970) 1054-1070
67. Zaikin A.D., Golubev D.S., van Otterlo A., and Zimányi G.T. Quantum phase slips and transport in ultrathin superconducting wires. Phys. Rev. Lett. 78 (1997) 1552-1555
68. Newbower R.S., Beasley M.R., and Tinkham M. Fluctuation effects on the superconducting transition of tin whisker crystals. Phys. Rev. B 5 (1972) 864-868
69. Lau C.N., Markovic N., Bockrath M., Bezryadin A., and Tinkham M. Quantum phase slips in superconducting nanowires. Phys. Rev. Lett. 87 (2001) 217003
70. Ao P., and Zhu X.-M. Microscopic theory of vortex dynamics in homogeneous superconductors. Phys. Rev. B 60 (1999) 6850-6877
71. Greene J.M. Geometrical properties of three-dimensional reconnecting magnetic fields with nulls. J. Geophys. Res. 93 (1988) 8583-8590
72. Lau Y.-T., and Finn J.M. Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines. Astrophys. J. 350 (1990) 672-691
73. Eyink G.L. Locality of turbulent cascades. Physica D 207 (2005) 91-116
74. Eyink G.L. Multi-scale gradient expansion of the turbulent stress tensor. J. Fluid Mech. 549 (2006) 159-190
75. Mandelbrot B.B. Géométrie fractale de la turbulence. Dimension de Hausdorff, dispersion et nature des singularités du mouvement des fluides. C. R. Paris 282A (1976) 119-120
76. Sreenivasan K.R., and Meneveau C. The fractal facets of turbulence. J. Fluid Mech. 173 (1986) 357-386
77. Fung J.C.H., and Vassilicos J.C. Fractal dimensions of lines in chaotic advection. Phys. Fluids A 3 (1991) 1433
78. Villermaux E., and Gagne Y. Line dispersion in homogeneous turbulence: stretching, fractal dimensions, and micromixing. Phys. Rev. Lett. 73 (1994) 252-255
79. Kivotides D. Geometry of turbulent tangles of material lines. Phys. Lett. A 318 (2003) 574-578
80. Nicolleau F.C.G.A., and Elmaihy A. Study of the development of three-dimensional sets of fluid particles and iso-concentration fields using kinematic simulation. J. Fluid Mech. 517 (2004) 229-249
81. Young L.C. An inequality of the Hölder type, connected with Stieltjes integration. Acta Math. 67 (1936) 251-282
82. Young L.C. General inequalities for Stieltjes integrals and the convergence of Fourier series. Math. Ann. 115 (1938) 581-612
83. Kazantsev A.P. Enhancement of a magnetic field by a conducting fluid. Sov. Phys. JETP 26 (1968) 1031-1034
84. Kraichnan R.H. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11 (1968) 945-953
85. Vincenzi D. The Kraichnan-Kazantsev dynamo. J. Stat. Phys. 106 (2002) 1073-1091
86. Boldyrev S., and Cattaneo F. Magnetic-field generation in Kolmogorov-turbulence. Phys. Rev. Lett. 92 (2004) 144501
87. Celani A., Mazzino A., and Vincenzi D. Magnetic field transport and kinematic dynamo effect: a Lagrangian interpretation. Proc. R. Soc. A 462 (2006) 137-147
88. Grauer R., Krug J., and Marliani C. Scaling of high-order structure functions in magnetohydrodynamic turbulence. Phys. Lett. A 195 (1994) 335-338
89. Politano H., and Pouquet A. Model of intermittency in magnetohydrodynamic turbulence. Phys. Rev. E 52 (1995) 636-641
90. Horbury T.S., and Balogh A. Structure function measurements of the intermittent MHD turbulent cascade. Nonlinear Proc. Geophys. 4 (1997) 185-199
91. Müller W.-C., and Biskamp D. Scaling properties of three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 84 (2000) 475-478
92. Richardson L.F. Atmospheric diffusion shown on a distance-neighbor graph. Proc. R. Soc. Lond. Ser. A 110 (1926) 709-737
93. Bernard D., Gawȩdzki K., and Kupiainen A. Slow modes in passive advection. J. Stat. Phys. 90 (1998) 519-569
94. Chaves M., Gawȩdzki K., Horvai P., Kupiainen A., and Vergassola M. Lagrangian dispersion in Gaussian self-similar velocity ensembles. J. Stat. Phys. 113 (2003) 643-692
95. Le Jan Y., and Raimond O. Integration of Brownian vector fields. Ann. Probab. 30 (2002) 826-873
96. Le Jan Y., and Raimond O. Flows, coalescence, and noise. Ann. Probab. 32 (2004) 1247-1315