Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind

Nonlinear Processes in Geophysics

Volumn 4, Issue 2, 1997, Pages 101-124

  Marsch, E ^a   Tu, C Y ^a,b  

^a MAX PLANCK INSTITUT FÜR SONNENSYSTEMFORSCHUNG   (Germany)

^b PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001276938     PISSN: 10235809     EISSN: None     Source Type: Journal    
DOI: 10.5194/npg-4-101-1997     Document Type: Article

References (98)

1. Anselmet, F., Gagne, Y., Hopfinger, E. J., and Antonia, R. A., High-order velocity structure functions in turbulent shear flows, J. Fluid Mech., 140, 63-89, 1984.
2. Batchelor, G. K., Theory of Homogeneous Turbulence, Cambridge University Press, 1953.
3. Bavassano, B., Dobrowolny, M., Mariani, F., and Ness, N. F., On the polarization state of hydromagnetic fluctuations in the solar wind, J. Geophys. Res., 86, 1271, 1981.
4. Bavassano, B., Dobrowolny, M., Mariani, F., and Ness, N. F., Radial evolution of power spectra of interplanetary Alfvénic turbulence, J. Geophys. Res., 87, 3617-3622, 1982a.
5. Bavassano, B., Dobrowolny, M., Fanfoni, G., Mariani, F., and Ness, N. F., Statistical properties of MHD fluctuations associated with high-speed streams from Helios-2 observations, Solar Phys., 78, 373-384, 1982b.
6. Belcher, J. W. and Davis, L., Large-amplitude Alfvén waves in the interplanetary medium, J. Geophys. Res., 76, 3534-3563, 1971.
7. Benzi, B., Paladin, G., Parisi, G., and Vulpiani, A., On the multifractal nature of fully developed turbulence and chaotic systems, J. Phys. A: Math. Nucl. Gen., 77, 3521, 1984.
8. Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., and Succi, S., Extended self-similarity in turbulent flows, Phys.Rev. E, 48, R29, 1993.
9. Berry, Diffractals, J. Phys. A: Math. Gen., 12, 781, 1979.
10. Biskamp, D., Welter, H., and Walter, M., Statistical properties of two-dimensional turbulence, Phys. Fluids, B2, 3024, 1990.
11. Biskamp, D., Nonlinear Magnetohydrodynamics, Cambridge University Press, p. 194 and p. 228, 1993.
12. Borgas, M. S., A comparison of intermittency models in turbulence, Phys. Fluids A, 4, 2055-2061, 1992.
13. Burlaga, L. F. and Ogilvie, K. W., Magnetic and thermal pressures in the solar wind, Solar Physics, 15, 61-71, 1970.
14. Burlaga, L. F., MHD processes in the outer heliosphere, Space Sci. Rev., 39, 255, 1984.
15. Burlaga, L. F. and Klein, L. W., Fractal structure of the interplanetary magnetic field, J. Geophys. Res., 91, 347-350, 1986.
16. Burlaga, L. F., Intermittent turbulence in the solar wind, J. Geophys. Res., 96, 5847-5851, 1991a.
17. Burlaga, L. F., Multifractal structure of the interplanetary magnetic field: Voyager 2 observations near 25 AU, 1987 - 1988, Geophys. Res. Lett., 18, 69-72, 1991b.
18. Burlaga, L. F., Multifractal Structure of speed fluctuations in recurrent streams at 1 AU and near 6 AU, Geophys. Res. Lett., 18, 1651-1654, 1991c.
19. Burlaga, L. F., Multifractal structure of the magnetic field and plasma in recurrent streams at 1 AU, J. Geophys. Res., 97, 4283, 1992.
20. Burlaga, L. F., Intermittent turbulence in large-scale velocity fluctuations at 1 AU near solar maximum, J. Geophys. Res., 98, 17467, 1993.
21. Carbone, V., Cascade model for intermittency in fully developed magnetohydrodynamic turbulence, Phys. Rev. Letts., 71, 1546-1548, 1993.
22. Carbone, V., Scaling exponents of the velocity structure functions in the interplanetary medium, Ann. Geophys., 72, 585-590, 1994.
23. Carbone, V., Signed measures in a shell model for hydromagnetic turbulence, Europhys. Lett., 29 (5), 377-382, 1995.
24. Carbone, V., Veltri, P., and Bruno, R., Experimental evidence for differences in the extended self-similarity scaling laws between fluid and magnetohydrodynamic turbulent flows, Phys. Rev. Lett., 75, 3110, 1995.
25. Carbone, V. and Bruno, R., Cancellation exponents and multifractal scaling laws in the solar wind magnetohydrodynamic turbulence, Ann. Geophys., 14, 777, 1996.
26. Carbone, V., Bruno, R., and Veltri, P., Evidence for extended self-similarity in hydromagnetic turbulence, Geophys. Res. Lett., 23, 121-124, 1996.
27. Denskat, K. U. and Neubauer, F. M., Statistical properties of low-frequency magnetic field fluctuations in the solar wind from 0.29 to 1.0 AU during solar minimum conditions: Helios 1 and Helios 2, J. Geophys. Res., 87, 2215-2223, 1982.
28. Dobrowolny, M., Mangeney, A., and Veltri, P., Fully developed anisotropic turbulence in interplanetary space, Phys. Rev. Lett., 45, 144-147, 1980.
29. Dudok de Wit, T. and Krasnosel'skikh, V.V., Non-Gaussian statistics in space plasma turbulence: fractal properties and pitfalls, Nonlinear Processes in Geophysics, 3, 262-273, 1996.
30. Eckman, J. P. and Ruelle, D., Ergodic theory of chaos and strange attractors, Rev. Mod. Phys., 57, 617, 1985.
31. Elsässer, W. M., The hydromagnetic equations, Phys. Rev., 79, 183, 1950.
32. Feder, J., Fractals, Plenum, New York, 1988.
33. Feynman, J. and Ruzmaikin, A., Distributions of the interplanetary field revisited, J. Geophys. Res., 99, 17645, 1994.
34. Frisch, U., Sulem, P. L., and Nelkin, M., A simple dynamical model of intermittent fully developed turbulence, J. Fluid Mech., 87, 719-736, 1978.
35. Frisch, U. and Parisi, G., in Turbulence and Predictibility in Geophysical Fluid Dynamics and Climate Dynamics, Eds. M. Ghil, R. Benzi and G. Parisi, North Holland, New York, p. 84, 1983.
36. Frisch, U., Turbulence, Cambridge University Press, 1995.
37. Goldstein M. L., Roberts, D. A., and Matthaeus, W. H., Magnetohydrodynamic turbulence in cosmic winds, Proceedings of the Tuscon conference on "Cosmic Winds and the Heliosphere", in press, 1993.
38. Grappin, R., Mangeney, A., and Marsch, E., On the origin of solar wind MHD turbulence: Helios data revisited, J. Geophys. Res., 95, 8197-8209, 1990.
39. Grappin, R., Velli, M., and Mangeney, A., "Alfvénic" versus "standard" turbulence in the solar wind, Ann. Geophysicae, 9, 416-426, 1991.
40. Grappin, R., 1994. "Sommerschule Aquila"
41. Grauer, R., Krug, J., and Marliani, C., Scaling of higher-order structure functions in magnetohydrodynamic turbulence, Physics Letters A, 195, 335-338, 1994.
42. Grauer, R. and Marliani, C., Numerical and analytical estimates for the structure functions in two-dimensional magnetohydrodynamic flows, Phys. Plasmas, 2 (1), 41-47, 1995.
43. Grauer, R. and Marliani, C., Analytical and numerical approaches to structure functions in magnetohydrodynamic turbulence, Physica Scripta, T67, 38-42, 1996.
44. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I., Fractal measures and their singularities: The characterization of strange sets, Phys. Rev., A 33, 1141, 1986.
45. Hentschel, H. G. E. and Procaccia, I., The infinite number of generalized dimensions of fractals and strange attractors, Physica, 8D, 435, 1983.
46. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Ulysses magnetic field observations of fluctuations within polar coronal flows, Ann. Geophysicae, 13, 105-107, 1995a.
47. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Observations of evolving turbulence in the polar solar wind, Geophy. Res. Lett., 22, 3401-3404, 1995b.
48. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Anisotropy of inertial range turbulence in the solar heliosphere, Geophy. Res. Lett., 22, 3405-3408, 1995c.
49. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Magnetic field signatures of unevolved turbulence in solar polar flows, J. Geophys. Res., 101, 405-413, 1996.
50. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Intermittent heliospheric turbulence, J. Geophys. Res., submitted, 1997a.
51. Horbury, T. A., Balogh, A., Forsyth, R. J., and Smith, E. J., Ulysses ob-servations of intermittent heliospheric turbulence, Adv. Space Phys., 19, 847-850, 1997b.
52. Iroshnikov, P. S., Turbulence of conducting fluids in a strong magnetic field, Sov. Astron., 7, 566, 1964.
53. Karl, J., Pätzold, M., and Bird, M.K., Coronal radio sounding: Non-Gaussian turbulence in the source regions of slow and fast solar wind, Geophys. Res. Lett., 24,2881-2884,1997.
54. Klein, L. W., Roberts, D. A., and Goldstein, M. L., Anisotropy and minimum variance directions of solar wind fluctuations in the outer heliosphere, J. Geophys. Res., 96, 3779-3788, 1991.
55. Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Compt. Rend. Acad. Sci., U.R.S.S., 30, 301, 1941.
56. Kolmogorov, A. N., A refinement of previous hypothesis concerning the local structure of turbulence in viscous incompressible fluid at high Reynolds number, J. Fluid Mech., 13, 82, 1962.
57. Kraichnan, R. H., Inertial-range spectrum of hydromagnetic turbulence, Phys. Fluids, 8, 1385-1387, 1965.
58. Kraichnan, R. H., Models of intermittency in hydrodynamic turbulence, Phys. Rev. Lett., 65, 575-578, 1990.
59. Lesieur, M., Turbulence in Fluids, Third Revised and Enlarged Edition, Kluwer Academic Publishers, Doordrecht, The Netherlands, 1997.
60. Mangeney, A., Grappin, R., and Velli, M., MHD Turbulence in the Solar Wind, in Proc. MHD Symposium, Advances in Solar System Magnetohydrodynamics, E.R. Priest and A.W. Hood (Eds.), St. Andrews, Scotland, Cambridge University Press, p. 327, 1991.
61. Marsch, E. and Mangeney, A., Ideal MHD equations in terms of compressive Elsässer variables, J. Geophys. Res., 92, 7363-7367, 1987.
62. Marsch, E. and Tu, C.-Y, On the radial evolution of MHD turbulence in the inner heliosphere, J. Geophys. Res., 95, 8211-8229, 1990a.
63. Marsch, E. and Tu, C.-Y, Spectral and spatial evolution of compressive turbulence in the inner solar wind, J. Geophys. Res., 95, 11945-11956, 1990b.
64. Marsch, E., Kinetic physics of the solar wind plasma, in Physics of the Inner Heliosphere, Vol. I, Eds. R. Schwenn und E. Marsch, Springer-Verlag, Heidelberg, pp 45-133, 1991a.
65. Marsch, E., MHD Turbulence in the Solar Wind, in Physics of the Inner Heliosphere, Vol. II, Eds. R. Schwenn and E. Marsch, Springer Verlag, Heidelberg, pp 159-241, 1991b.
66. Marsch, E., Tu, C.-Y., Liu, S., and Rosenbauer, H., Spectra and structure functions of temperature fluctuations in the inner solar wind, ESA SP-346, 315-320, 1992.
67. Marsch, E. and Liu, S., Structure functions and intermittency of velocity fluctuations in the inner solar wind, Ann. Geophysicae, 11, 227-238, 1993.
68. Marsch, E. and Tu, C.-Y., Correlations between the fluctuations of pressure, density, temperature and magnetic field in the solar wind, Ann. Geophysicae, 11, 659, 1993.
69. Marsch, E. and Tu, C.-Y, Turbulence in the solar wind, in Spatio-Temporal Analysis for Resolving Plasma Turbulence (START), Proceedings ESA WPP-047, 11-18, 1993.
70. Marsch, E. and Tu, C-Y, Non-Gaussian probability distributions of solar wind fluctuations, Ann. Geophysicae, 12, 1127, 1994.
71. Marsch, E., Tu, C.-Y, and Rosenbauer, H., Multifractal scaling of the kinetic energy flux in solar wind turbulence, Ann. Geophysicae, 14, 259-269, 1996.
72. Matthaeus, W. H., Goldstein, M. L., and King, J. H., An interplanetary magnetic field ensemble, J. Geophys. Res., 91, 59-69, 1986.
73. Matthaeus, W. H., Goldstein, M. L., and Roberts, D. A., Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind, J. Geophys. Res., 95, 20673-20683, 1990.
74. McComb, W. D., The physics of fluid turbulence, Oxford University Press, Oxford, 1990.
75. Meneveau, C. and Sreenivasan, K. R., The multifractal spectrum of the dissipation field in turbulent flow, Nuclear Physics, B 2, 49-76a, 1987.
76. Meneveau, C. and Sreenivasan, K. R., Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett., 59, 1424-1427, 1987b.
77. Meneveau, C and Sreenivasan, K. R., The multifractal nature of turbulent energy dissipation, J. Fluid Mech., 224, 429-484, 1991.
78. Monin, A. S. and Yaglom, A. M., Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. I+II, The MIT Press, Cambridge, USA, 1975.
79. Montgomery, D. M., Theory of hydromagnetic turbulence, in Solar Wind Five, edited by M. Neugebauer, NASA Conference Publication 2280, Washington, USA, 107-130, 1983.
80. Paladin, G. and Vulpiani, A., Anomalous scaling laws in multifractal objects, Physics Reports, 156, 147-225, 1987.
81. Politano, H. and Pouquet, A., Von Kármán-Howarth equation for magnetohydrodynamic fluids and its consequences on third-order longitudinal structure and correlation functions, Phys. Rev. E, in press, 1997.
82. Polygiannakis J. M. and Moussas, X., Fractal properties of the interplanetary magnetic field fluctuations: indications of chaotic dynamics, Astron. Astrophys., 283, 990, 1994.
83. Roberts, D. A. and Goldstein, M. L., Turbulence and waves in the solar wind, Reviews of Geophysics, Supplement, 932-943, 1991.
84. Roberts, D. A., Gosh, S., Goldstein, M. L., and Matthaeus, W. H., Magnetohydrodynamic Simulation of the Radial Evolution and Stream Structure of Solar-Wind Turbulence, Phys. Rev. Lett., 67, 3741-3744, 1991.
85. Rose, H. A. and Sulem, P. L., Fully developed turbulence and statistical mechanics, Le Journal de Physique, 139, 441-484, 1978.
86. Ruzmaikin, A., Lyannaya, I. R., Styashkin, V. A., and Yeroshenko, E., The spectrum of the interplanetary magnetic field near 1.3 AU, J. Geophys. Res., 98, 13303-13306, 1993.
87. Ruzmaikin, A., Feynman, J., Goldstein, B. E., Smith, E. J., and Balogh, A., Intermittent turbulence in solar wind from the south polar hole, J. Geophys. Res., 100, 3395, 1995.
88. Sreenivasan, K. R. and Antonia, R. A., The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech., 29, 435-472, 1997.
89. She, Z.-S. and Lévéque, E., Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., 72, 336, 1994.
90. Tel, T., Fractals, Multifractals, and Thermodynamics, An Introductory Review, Z. Naturforschung, 43a, 1154, 1988.
91. Tu, C.-Y, Pu, Z.-Y, and Wei, F.-S., The power spectrum of interplanetary Alfvénic fluctuations: Derivation of the governing equations and its solution, J. Geophys. Res., 89, 9695-9702, 1984.
92. Tu, C.-Y., The damping of interplanetary Alfvénic fluctuations and the heating of the solar wind, J. Geophys. Res., 93, 7-20, 1988.
93. Tu, C.-Y, Marsch, E. and Thieme, K. M., Basic properties of solar wind MHD turbulence near 0.3 AU analysed by means of Elsässer Variables, J. Geophys. Res., 94, 11739-11759, 1989.
94. Tu, C.-Y. and Marsch, E., A case study of very low cross-helicity fluctuations in the solar wind, Ann. Geophysicae, 9, 319-332, 1991.
95. Tu, C.-Y. and Marsch, E., MHD structures, waves and turbulence in the solar wind: Observations and theories, Space Science Reviews, 73, 1-210, 1995.
96. Tu, C.-Y, Marsch, E., and Rosenbauer, H., An extended structure function model and its application to the analysis of solar wind intermittency properties, Ann. Geophys., 14, 270-285, 1996.
97. Vincent, A. and Meneguzzi, M., The spatial structure and statistical properties of homogeneous turbulence, J. Fluid Mech., 225, 1-20, 1991.
98. Whang, Y.C., Probability distribution functions of microscale magnetic fluctuations during quiet conditions, Solar Phys., 53, 507, 1977.