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A Natural Wind Tunnel

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Turbulence in the Solar Wind

Part of the book series: Lecture Notes in Physics ((LNP,volume 928))

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Abstract

The solar wind has been used as a wind tunnel by Burlaga who, at the beginning of the 1990s, started to investigate anomalous fluctuations (Burlaga 1991a,c,b, 1995) as observed by measurements in the outer heliosphere by the Voyager spacecraft. In 1991, Marsch (1992), in a review on solar wind turbulence given at the Solar Wind Seven conference, underlined the importance of investigating scaling laws in the solar wind and we like to report his sentence: “The recent work by Burlaga (1991a,c) opens in my mind a very promising avenue to analyze and understand solar wind turbulence from a new theoretical vantage point.

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Notes

  1. 1.

    Since the solar wind moves at supersonic speed V sw, the usual Taylor’s hypothesis is verified, and we can get information on spatial scaling laws ℓ by using time differences τ = ℓ∕V sw.

  2. 2.

    Note that, according to the occurrence of the Yaglom’s law, that is a third-order moment is different from zero, the fluctuations at a given scale in the inertial range must present some non-Gaussian features. From this point of view the calculation of structure functions with the absolute value is unappropriate because in this way we risk to cancel out non-Gaussian features. Namely we symmetrize the probability density functions of fluctuations. However, in general, the number of points at disposal is much lower than required for a robust estimate of odd structure functions, even in usual fluid flows. Then, as usually, we will obtain structure functions by taking the absolute value, even if some care must be taken in certain conclusions which can be found in literature.

References

  • R. Benzi, G. Paladin, A. Vulpiani, G. Parisi, On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A: Math. Gen. 17, 3521–3531 (1984). doi:10.1088/0305-4470/17/18/021

    Article  ADS  MathSciNet  Google Scholar 

  • R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Extended self-similarity in turbulent flows. Phys. Rev. E 48, 29–35 (1993). doi:10.1103/PhysRevE.48.R29

    Article  ADS  Google Scholar 

  • D. Biskamp, Nonlinear Magnetohydrodynamics. Cambridge Monographs on Plasma Physics, vol. 1 (Cambridge University Press, Cambridge, 1993)

    Google Scholar 

  • D. Biskamp, Cascade models for magnetohydrodynamic turbulence. Phys. Rev. E 50, 2702–2711 (1994). doi:10.1103/PhysRevE.50.2702

    Article  ADS  Google Scholar 

  • D. Biskamp, Magnetohydrodynamic Turbulence (Cambridge University Press, Cambridge, 2003)

    Book  MATH  Google Scholar 

  • G. Boffetta, V. Carbone, P. Giuliani, P. Veltri, A. Vulpiani, Power laws in solar flares: self-organized criticality or turbulence? Phys. Rev. Lett. 83, 4662–4665 (1999). doi:10.1103/PhysRevLett.83.4662

    Article  ADS  Google Scholar 

  • L.F. Burlaga, Intermittent turbulence in the solar wind. J. Geophys. Res. 96 (15), 5847–5851 (1991a). doi:10.1029/91JA00087

    Article  ADS  Google Scholar 

  • L.F. Burlaga, Multifractal structure of speed fluctuations in recurrent streams at 1 AU and near 6 AU. Geophys. Res. Lett. 18, 1651–1654 (1991b). doi:10.1029/91GL01221

    Article  ADS  Google Scholar 

  • L.F. Burlaga, Multifractal structure of the interplanetary magnetic field: Voyager 2 observations near 25 AU, 1987–1988. Geophys. Res. Lett. 18, 69–72 (1991c). doi:10.1029/90GL02596

    Article  ADS  Google Scholar 

  • L.F. Burlaga, Interplanetary Magnetohydrodynamics. International Series on Astronomy and Astrophysics, vol. 3 (Oxford University Press, New York, 1995)

    Google Scholar 

  • V. Carbone, Cascade model for intermittency in fully developed magnetohydrodynamic turbulence. Phys. Rev. Lett. 71, 1546–1548 (1993). doi:10.1103/PhysRevLett.71.1546

    Article  ADS  Google Scholar 

  • V. Carbone, R. Bruno, P. Veltri, Evidences for extended self-similarity in hydromagnetic turbulence. Geophys. Res. Lett. 23, 121–124 (1996a). doi:10.1029/95GL03777

    Article  ADS  Google Scholar 

  • V. Carbone, P. Veltri, R. Bruno, Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws. Nonlinear Process. Geophys. 3, 247–261 (1996b). doi:10.5194/npg-3-247-1996

    Article  ADS  Google Scholar 

  • V. Carbone, L. Sorriso-Valvo, E. Martines, V. Antoni, P. Veltri, Intermittency and turbulence in a magnetically confined fusion plasma. Phys. Rev. E 62, 49–56 (2000). doi:10.1103/PhysRevE.62.R49

    Article  ADS  Google Scholar 

  • V. Carbone, R. Marino, L. Sorriso-Valvo, A. Noullez, R. Bruno, Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations. Phys. Rev. Lett. 103 (6) (2009). doi:10.1103/PhysRevLett.103.061102

    Google Scholar 

  • B. Castaing, Y. Gagne, V. Hopfinger, Velocity probability density functions of high Reynolds number turbulence. Physica D 46, 177–200 (2001)

    Article  ADS  MATH  Google Scholar 

  • M. Dobrowolny, A. Mangeney, P. Veltri, Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45, 144–147 (1980). doi:10.1103/PhysRevLett.45.144

    Article  ADS  MathSciNet  Google Scholar 

  • T. Dudok de Wit, Can high-order moments be meaningfully estimated from experimental turbulence measurements? Phys. Rev. E 70 (2004). doi:10.1103/PhysRevE.70.055302

    Google Scholar 

  • M.A. Forman, C.W. Smith, B.J. Vasquez, Comment on ‘scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations’. Phys. Rev. Lett. 104 (18) (2010). doi:10.1103/PhysRevLett.104.189001

    Google Scholar 

  • U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  • U. Frisch, P.-L. Sulem, M. Nelkin, A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736 (1978). doi:10.1017/S0022112078001846

    Article  ADS  MATH  Google Scholar 

  • P. Giuliani, V. Carbone, A note on shell models for MHD turbulence. Europhys. Lett. 43, 527–532 (1998). doi:10.1209/epl/i1998-00386-y

    Article  ADS  Google Scholar 

  • C. Gloaguen, J. Léorat, A. Pouquet, R. Grappin, A scalar model for MHD turbulence. Physica D 17, 154–182 (1985). doi:10.1016/0167-2789(85)90002-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Y. Hattori, A. Ishizawa, Characteristic time scales and energy transfer in MHD turbulence, in IUTAM Symposium on Geometry and Statistics of Turbulence, ed. by T. Kambe, T. Nakano, T. Miyauchi. Fluid Mechanics and Its Applications, vol. 59 (Kluwer, Dordrecht, 2001), pp. 89–94

    Google Scholar 

  • H.G.E.F. Hentschel, I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractor. Physica D 8, 435–444 (1983). doi:10.1016/0167-2789(83)90235-X

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • G.G. Katul, C.I. Hsieh, J. Sigmon, Energy-inertial scale interaction for temperature and velocity in the unstable surface layer. Bound.-Layer Meteorol. 82, 49–80 (1997). doi:10.1023/A:1000178707511

    Article  ADS  Google Scholar 

  • A.N. Kolmogorov, The local structure turbulence in incompressible viscous fluids for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301–305 (1941)

    ADS  Google Scholar 

  • R.H. Kraichnan, On Kolmogorov’s inertial-range theories. J. Fluid Mech. 62, 305–330 (1974). doi:10.1017/S002211207400070X

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • L.D. Landau, E.M. Lifshitz, Physique Théorique. Mécanique des fluides, vol. 6 (Editions MIR, Moscow, 1971)

    Google Scholar 

  • M.-M. Mac Low, R.S. Klessen, Control of star formation by supersonic turbulence. Rev. Mod. Phys. 76, 125–194 (2004). doi:10.1103/RevModPhys.76.125

    Article  ADS  Google Scholar 

  • B.T. MacBride, C.W. Smith, M.A. Forman, The turbulent cascade at 1 AU: energy transfer and the third-order scaling for MHD. Astrophys. J. 679, 1644–1660 (2008). doi:10.1086/529575

    Article  ADS  Google Scholar 

  • B.T. MacBride, C.W. Smith, B.J. Vasquez, Inertial-range anisotropies in the solar wind from 0.3 to 1 AU: Helios 1 observations. J. Geophys. Res. 115 (A14), 7105 (2010). doi:10.1029/2009JA014939

    Google Scholar 

  • E. Marsch, Introduction to kinetic physics, waves and turbulence in the solar wind, in Solar Wind Seven, ed. by E. Marsch, R. Schwenn. COSPAR Colloquia Series, vol. 3 (Pergamon Press, Oxford, 1992), pp. 499–504

    Google Scholar 

  • C. Meneveau, Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469–520 (1991). doi:10.1017/S0022112091003786

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • E.A. Novikov, Scale similarity for random fields. Sov. Phys. Dokl. 14, 104–107 (1969)

    ADS  Google Scholar 

  • F. Okkels, The intermittent dynamics in turbulent shell models, Master’s Thesis, University of Copenhagen, Copenhagen, 1997

    Google Scholar 

  • F. Plunian, R. Stepanov, P. Frick, Shell models of magnetohydrodynamic turbulence. Phys. Rep. 523, 1–60 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  • H. Politano, A. Pouquet, Model of intermittency in magnetohydrodynamic turbulence. Phys. Rev. E 52, 636–641 (1995). doi:10.1103/PhysRevE.52.636

    Article  ADS  Google Scholar 

  • H. Politano, A. Pouquet, von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57, 21–25 (1998). doi:10.1103/PhysRevE.57.R21

    Google Scholar 

  • H. Politano, A. Pouquet, V. Carbone, Determination of anomalous exponents of structure functions in two-dimensional magnetohydrodynamic turbulence. Europhys. Lett. 43, 516–521 (1998). doi:10.1209/epl/i1998-00391-2

    Article  ADS  Google Scholar 

  • S.B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000)

    Book  MATH  Google Scholar 

  • G. Ruíz-Chavarría, C. Baudet, S. Ciliberto, Extended self similarity of passive scalars in fully developed turbulence. Europhys. Lett. 32, 319 (1995)

    Article  ADS  Google Scholar 

  • C. Salem, A. Mangeney, S.D. Bale, P. Veltri, Solar wind magnetohydrodynamics turbulence: anomalous scaling and role of intermittency. Astrophys. J. 702, 537–553 (2009). doi:10.1088/0004-637X/702/1/537

    Article  ADS  Google Scholar 

  • Z.-S. She, E. Leveque, Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336–339 (1994). doi:10.1103/PhysRevLett.72.336

    Article  ADS  Google Scholar 

  • C.W. Smith, J.E. Stawarz, B.J. Vasquez, M.A. Forman, B.T. MacBride, Turbulent cascade at 1 AU in high cross-helicity flows. Phys. Rev. Lett. 103 (20) (2009). doi:10.1103/PhysRevLett.103.201101

    Google Scholar 

  • L. Sorriso-Valvo, R. Marino, V. Carbone, A. Noullez, F. Lepreti, P. Veltri, R. Bruno, B. Bavassano, E. Pietropaolo, Observation of inertial energy cascade in interplanetary space plasma. Phys. Rev. Lett. 99 (11) (2007). doi:10.1103/PhysRevLett.99.115001

    Google Scholar 

  • L. Sorriso-Valvo, V. Carbone, R. Marino, A. Noullez, R. Bruno, P. Veltri, Sorriso-valvo et al. reply. Phys. Rev. Lett. 104 (18) (2010). doi:10.1103/PhysRevLett.104.189002

    Google Scholar 

  • H. Tennekes, J. Wyngaard, The intermittent small-scale structure of turbulence: data-processing hazards. J. Fluid Mech. 55, 93 (1972). doi:10.1017/S0022112072001661

    Article  ADS  Google Scholar 

  • C.-Y. Tu, E. Marsch, MHD structures, waves and turbulence in the solar wind: observations and theories. Space Sci. Rev. 73 (1/2), 1–210 (1995). doi:10.1007/BF00748891

    Article  ADS  Google Scholar 

  • B.J. Vasquez, C.W. Smith, K. Hamilton, B.T. MacBride, R.J. Leamon, Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU. J. Geophys. Res. 112 (A11), 7101 (2007). doi:10.1029/2007JA012305

    Google Scholar 

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Authors and Affiliations

  1. Fisica dei Plasmi Spaziali, INAF - Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy

    Roberto Bruno

  2. Dipartimento di Fisica, Università della Calabria, Rende (CS), Italy

    Vincenzo Carbone

Authors
  1. Roberto Bruno
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  2. Vincenzo Carbone
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Bruno, R., Carbone, V. (2016). A Natural Wind Tunnel. In: Turbulence in the Solar Wind. Lecture Notes in Physics, vol 928. Springer, Cham. https://doi.org/10.1007/978-3-319-43440-7_6

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