Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 15 4 2008 10.5194/npg-15-607-2008 http://www.nonlin-processes-geophys.net/15/607/2008/ http://www.nonlin-processes-geophys.net/15/607/2008/npg-15-607-2008.html http://www.nonlin-processes-geophys.net/15/607/2008/npg-15-607-2008.pdf 607 613 2008-07-28 Statistical analysis of transfer of fluctuations in solar wind turbulence M. Strumik maro@cbk.waw.pl W. M. Macek Space Research Centre, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warsaw, Poland Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland We present results of statistical analysis of the transfer of fluctuations in solar wind turbulence. We investigate the dynamics of the slow solar wind using an approach based on the Markov processes theory and experimental data measured by ACE spacecraft. In particular, we test whether the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We consider the following cases of transfer of fluctuations: magnetic-to-magnetic, velocity-to-velocity, velocity-to-magnetic, and magnetic-to-velocity. In all these cases, the obtained results confirm local character of the transfer of fluctuations. Alexakis, A., Mininni, P D., and Pouquet, A.: Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence, Phys. Rev. E, 72, 046301, 2005. Biskamp, D.: Magnetohydrodynamic Turbulence, Cambridge: University Press, 2003. Bruno, R. and Carbone, V.: The Solar Wind as a Turbulence Laboratory, Living Reviews in Solar Physics, 2, 4, 2005. Burlaga, L F.: Multifractal structure of the interplanetary magnetic field – Voyager 2 observations near 25 AU, 1987–1988, Geophys. Res. Lett., 18, 69–72, 1991. Burlaga, L F.: Lognormal and multifractal distributions of the heliospheric magnetic field, J. Geophys. Res., 106, 15917–15928, 2001. Davoudi, J. and Tabar, M R.: Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades, Phys. Rev. Lett., 82, 1680–1683, 1999. Debliquy, O., Verma, M K., and Carati, D.: Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamic turbulence, Phys. Plasmas, 12, 2309, 2005. Friedrich, R. and Peinke, J.: Statistical properties of a turbulent cascade, Physica D, 102, 147–155, 1997a. Friedrich, R. and Peinke, J.: Description of a Turbulent Cascade by a Fokker-Planck Equation, Phys. Rev. Lett., 78, 863–866, 1997b. Frisch, U.: Turbulence. The legacy of A.N. Kolmogorov, Cambridge: University Press, 1995. Goldstein, M L. and Roberts, D A.: Magnetohydrodynamic turbulence in the solar wind, Phys. Plasmas, 6, 4154–4160, 1999. Goldstein, M L., Roberts, D A., and Matthaeus, W H.: Magnetohydrodynamic Turbulence In The Solar Wind, Annu. Rev. Astron. Astrophys., 33, 283–326, 1995. Hnat, B., Chapman, S C., and Rowlands, G.: Intermittency, scaling, and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft, Phys. Rev. E, 67, 056404, 2003. Kishida, K., Araki, K., Kishiba, S., and Suzuki, K.: Local or Nonlocal? Orthonormal Divergence-Free Wavelet Analysis of Nonlinear Interactions in Turbulence, Phys. Rev. Lett., 83, 5487–5490, 1999. Macek, W M. and Szczepaniak, A.: Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett., 35, L02108, doi:10.1029/2007GL32263, 2008. Marsch, E. and Tu, C Y.: Non-Gaussian probability distributions of solar wind fluctuations, Ann. Geophys., 12, 1127–1138, 1994. 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. Matthaeus, W H. and Goldstein, M L.: Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind, J. Geophys. Res., 87, 6011–6028, 1982. McComas, D J., Bame, S J., Barker, P., Feldman, W C., Phillips, J L., Riley, P., and Griffee, J W.: Solar Wind Electron Proton Alpha Monitor (SWEPAM) for the Advanced Composition Explorer, Space Sci. Rev., 86, 563–612, 1998. Mininni, P., Alexakis, A., and Pouquet, A.: Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo, Phys. Rev. E, 72, 046302, 2005. Pedrizzetti, G. and Novikov, E A.: On Markov modelling of turbulence, J. Fluid Mech., 280, 69–93, 1994. Pouquet, A., Frisch, U., and Leorat, J.: Strong MHD helical turbulence and the nonlinear dynamo effect, J. Fluid Mech., 77, 321–354, 1976. Renner, C., Peinke, J., and Friedrich, R.: Experimental indications for Markov properties of small-scale turbulence, J. Fluid Mech., 433, 383–409, 2001. Risken, H.: The Fokker-Planck equation. Methods of solution and applications, Springer Series in Synergetics, Berlin, New York: Springer, 2nd ed., 1989. Schwenn, R.: Large-Scale Structure of the Interplanetary Medium, in: Physics of the Inner Heliosphere I. Large-Scale Phenomena, edited by Schwenn, R. and Marsch, E., pp. 99–182, Berlin: Springer-Verlag, 1990. Schwenn, R.: Solar Wind Sources and Their Variations Over the Solar Cycle, Space Sci. Rev., 124, 51–76, 2006. Smith, C W., L'Heureux, J., Ness, N F., Acuña, M H., Burlaga, L F., and Scheifele, J.: The ACE Magnetic Fields Experiment, Space Sci. Rev., 86, 613–632, 1998. Sorriso-Valvo, L., Carbone, V., Veltri, P., Consolini, G., and Bruno, R.: Intermittency in the solar wind turbulence through probability distribution functions of fluctuations, Geophys. Res. Lett., 26, 1801–1804, 1999. 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. Tu, C.-Y. and Marsch, E.: MHD structures, waves and turbulence in the solar wind: Observations and theories, Space Sci. Rev., 73, 1–210, 1995. Verma, M K., Ayyer, A., and Chandra, A V.: Energy transfers and locality in magnetohydrodynamic turbulence, Phys. Plasmas, 12, 2307, 2005.