Asymmetric multifractal model for solar wind intermittent turbulence

Nonlinear Processes in Geophysics

Volumn 15, Issue 4, 2008, Pages 615-620

  Szczepaniak, A ^a   MacEk, W M ^a,b  

^a Polish Academy of Sciences   (Poland)

^b CARDINAL STEFAN WYSZY SKI UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMMETRY; MEASUREMENT METHOD; MODELING; SOLAR WIND; TURBULENCE;

EID: 49049100882     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-15-615-2008     Document Type: Article

References (52)

1. Anselmet, E., 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. Benzi, R., Paladin, G., Vulpiani, A., and Parisi, G.: On the multi-fractal nature of fully developed turbulence and chaotic systems, J. Phys. A, 17, 3521-3531, 1984.
3. Biskamp, D.: Magnetohydrodynamic Turbulence, Cambridge, Cambridge University Press, 2003.
4. Borgas, M. S.: A comparison of intermittency models in turbulence, Phys. Fluids A, 4, 2055-2061, 1992.
5. Bruno, R., Carbone, V., and Sorriso-Valvo, L.: Radial evolution of solar wind intermittency in the inner heliosphere, J. Geoophys. Res., 108, 1130, doi:10.1029/2002JA009615, 2003.
6. Burlaga, L. E.: Intermittent turbulence in the solar wind, J. Geophys. Res., 96, 5847-5851, 1991a.
7. 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.
8. Burlaga, L. E.: Multifractal structure of speed fluctuations in recurrent streams at 1 AU and near 6 AU, Geophys. Res. Lett., 18, 1651-1654, 1991c.
9. Burlaga, L. F.: Multifractal structure of the magnetic field and plasma in recurrent streams at 1 AU, J. Geophys. Res., 97, 4283-4293, 1992a.
10. Burlaga, L. F.: Multifractals in the solar wind, in: Solar Wind Seven, edited by: Marsch, E. and Schwenn, R., Proceedings of the 3rd COSPAR Colloquium, Goslar, Germany, 16-20 September 1991, COSPAR Colloquia Series, vol. 3, 429-432, Pergamon Press, Oxford, 1992b.
11. Burlaga, L. F.: Intermittent turbulence in large-scale velocity fluctuations at 1 AU near solar maximum, J. Geophys. Res., 98, 17467-17474, 1993.
12. Burlaga, L. F.: Lognormal and multifractal distributions of the he-liospheric magnetic field, J. Geophys. Res., 106, 15917-15927, doi:10.1029/2000JA000107, 2001.
13. Burlaga, L. F.: Multifractal structure of the large-scale heliospheric magnetic field strength fluctuations near 85 AU, Nonlin. Processes Geophys., 11, 441-445, 2004, http://www.nonlin-processes-geophys.net/11/441/2004/.
14. Burlaga, L. F., Perko, L., and Pirraglia, J.: Cosmic-ray modulation, merged interaction regions, and multifractals, Astrophys. L., 407, 347-358, 1993.
15. Burlaga, L. F., Wang, C., and Ness, N. F.: A model and observations of the multifractal spectrum of the heliospheric magnetic field strength fluctuations near 40 AU, Geophys. Res. Lett., 30, 1543, doi:10.1029/ 2003GL016903, 2003.
16. Carbone, V.: Cascade model for intermittency in fully developed magnetohydrodynamic turbulence, Phys. Rev. Lett., 71, 1546-1548, 1993.
17. Carbone, V.: Scaling exponents of the velocity structure functions in the interplanetary medium, Ann. Geophys., 12, 585-590, 1994, http://www.ann- geophys.net/12/585/1994/.
18. Chhabra, A. and Jensen, R. V.: Direct determination of the f(α) singularity spectrum, Phys. Rev. Lett. 62, 1327-1330, 1989.
19. Chian, A. C.-L., Kamide, Y., Rempel, E. L., and Santana, W. M.: On the chaotic nature of solar-terrestrial environment: Interplanetary Alfvén intermittency, J. Geophys. Res., 111, A07S03, doi:10.1029/2005JA011396, 2006.
20. Frisch, U., Sulem, P.-L., and Nelkin, M.: A simple dynamical model of intermittent fully developed turbulence, J. Fluid Mech., 87, 719-736, 1978.
21. Frisch, U.: Turbulence, Cambridge, Cambridge University Press, 1995.
22. Goldstein, M. L. and Roberts, D. A.: Magnetohydrodynamic turbulence in the solar wind, Phys. Plasmas, 6, 4154-4160, 1999.
23. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaecia, I., and Shraiman, B. I.: Fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A, 33, 1141-1151, 1986.
24. Hentschel, H. G. E. and Procaecia, I.: The infinite number of generalized dimensions of fractals and strange attractors, PhysicaD, 8, 435-444, 1983.
25. Horbury, T. S., Balogh, A., Forsyth, R. J., and Smith, E. J.: ULYSSES observations of intermittent heliospheric turbulence, Adv. Space Res., 19(6), 847-850, 1997.
26. Horbury, T. S. and Balogh, A.: Structure function measurements of the intermittent MHD turbulent cascade, Nonlin. Processes Geophys., 4, 185-199, 1997, http://www.nonlin-processes-geophys.net/4/185/1997/.
27. Kolmogorov, A. N.: The local structure of turbulence in incompressible viscous fluid at very high Reynolds' numbers, Comptes rendus (Doklady) de l'Academie des Science de l'USSR, 30, 301-305, 1941.
28. Kolmogorov, A. N.: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech., 13, 82-85, 1962.
29. Kraichnan, R. H.: Inertial-range spectrum of hydromagnetic turbulence, Phys. Fluids, 8, 1385-1387, 1965.
30. Lesieur, M.: Turbulence in Fluids, 2nd edition, Dordrecht, Kluwer, 1990.
31. Macek, W. M.: Testing for an attractor in the solar wind flow, Phys-ica D, 122, 254-264, 1998.
32. Macek, W. M.: Multifractality and chaos in the solar wind, in: Experimental Chaos, edited by: Boccaletti, S., Gluckman, B. J., Kurths, J., Pecora, L. M., and Spano, M. L., 622, American Institute of Physics, New York, 74-79, 2002.
33. Macek, W. M.: The multifractal spectrum for the solar wind flow, in: Solar Wind 10, edited by: Velli, R., Bruno, R., and Malara, F., 679, American Institute of Physics, New York, 530-533, 2003.
34. Macek, W. M.: Modeling multifractality of the solar wind, Space Sci. Rev., 122, 329-337, doi:10.1007/s114214-006-8185-z, 2006.
35. Macek, W. M., Bruno, R., and Consolini, G.: Generalized dimensions for fluctuations in the solar wind, Phys. Rev. E, 72, 017202, doi:10.1103/PhysRevE. 72.017202, 2005.
36. Macek W. M., Bruno, R., and Consolini, G.: Testing for multifractality of the slow solar wind, Adv. Space Res., 37, 461-466, doi:10.1016/j.asr.2005.06. 057, 2006.
37. Macek, W. M.: Multifractality and intermittency in the solar wind, Nonlin. Processes Geophys., 14, 695-700, 2007, http://www.nonlin-processes- geophys.net/14/695/2007/.
38. Macek, W. M. and Szczepaniak, A.: Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett., 35, L02108, doi:10.1029/2007GL032263, 2008a.
39. Mandelbrot, B. B.: Multifractal measures, especially for the geophysicist, in: Pure Appl. Geophys., 131, Birkhauser Verlag, Basel, 5-42, 1989.
40. Marsch, E.: MHD turbulence in the solar wind physics of the inner heliosphere, edited by: Schwenn, R. and Marsch, E., Heidelberg, Springer-Verlag, 1991.
41. Marsch, E. and Liu, S.: Structure functions and intermittency of velocity fluctuations in the inner solar wind, Ann. Geophys., 11, 227-238, 1993, http://www.ann-geophys.net/ll/227/1993/.
42. Marsch, E. and Tu, C.-Y: Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind, Nonlin. Processes Geophys., 4, 101-124, 1997, http://ww w.nonlin-processes-geophys .net/4/101/1997/.
43. Marsch, E., Tu, C.-Y, and Rosenbauer, H.: Multifractal scaling of the kinetic energy flux in solar wind turbulence, Ann. Geophys., 14, 259-269, 1996, http://www.ann-geophys.net/14/259/1996/.
44. Meneveau, C. and Sreenivasan, K. R.: Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett., 59, 1424-1427, 1987.
45. Meneveau, C. and Sreenivasan, K. R.: The multifractal nature of turbulent energy dissipation, J. Fluid Mech., 224, 429-484, 1991.
46. Ott, E.: Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
47. Schwenn, R.: Large-scale structure of the interplanetary medium, in: Physics of the Inner Heliosphere, edited by: Schwenn, R. and Marsch, E., 20, Springer-Verlag, Berlin, 99-182, 1990.
48. She, Z.-S. and Leveque, E.: Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., 72, 336-339, 1994.
49. Sorriso-Valvo, L., Carbone, V., Giuliani, P., Veltri, P., Bruno, R., Antoni, V., and Martines, E.: Intermittency in plasma turbulence, Planet. Space Sci., 49, 1193-1200, 2001.
50. Sorriso-Valvo, L., Marino, R., Carbone, V., Lepreti, F., Veltri, P., Noullez, A., Bruno, R., Bavassano, B., and Pietropaolo, E.: Observation of inertial energy cascade in interplanetary space plasma, Phys. Rev. Lett., 99, 115001, doi:10.1103/PhysRevE.71.066313, 2007.
51. Stanley, H. E. and Meakin, P.: Multifractal phenomena in physics and chemistry, Nature, 335, 405-109, 1988.
52. Tsang, Y.-K., Ott, E., Antonsen Jr., T. M., and Guzdar, P. N.: Intermittency in two-dimensional turbulence with drag, Phys. Rev. E, 71, 066313, doi: 10.1103/PhysRevE.71.066313, 2005.