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Geophysical & Astrophysical Fluid Dynamics Volume 52, 1990 - Issue 1-3
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Original Articles

A shell model for anisotropic magnetohydrodynamic turbulence

Vincenzo Carbone Dipartimento di Fisica, Università della Calabria, Italy
&
Pierluigi Veltri Dipartimento di Fisica, Università della Calabria, Italy
Pages 153-181 | Received 25 Mar 1989, Published online: 19 Aug 2006

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Rodion Stepanov & Franck Plunian. (2006) Fully developed turbulent dynamo at low magnetic Prandtl numbers. Journal of Turbulence 7.
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Shadab Alam, Mahendra K. Verma & Pranav Joshi. (2023) Bolgiano-Obukhov spectrum and mixing efficiency in stably stratified turbulence. Physical Review E 107:5.
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O. Pezzi, F. Pecora, J. le Roux, N. E. Engelbrecht, A. Greco, S. Servidio, H. V. Malova, O. V. Khabarova, O. Malandraki, R. Bruno, W. H. Matthaeus, G. Li, L. M. Zelenyi, R. A. Kislov, V. N. Obridko & V. D. Kuznetsov. (2021) Current Sheets, Plasmoids and Flux Ropes in the Heliosphere. Space Science Reviews 217:3.
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Sean Oughton & N. Eugene Engelbrecht. (2021) Solar wind turbulence: Connections with energetic particles. New Astronomy 83, pages 101507.
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S. Oughton & W. H. Matthaeus. (2020) Critical Balance and the Physics of Magnetohydrodynamic Turbulence. The Astrophysical Journal 897:1, pages 37.
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Francesco Pegoraro & Pierluigi Veltri. (2020) The unusual properties of plasmas. La Rivista del Nuovo Cimento 43:5, pages 229-279.
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Teresa Maiorano, Adriana Settino, Francesco Malara, Oreste Pezzi, Francesco Pucci & Francesco Valentini. (2020) Kinetic Alfvén wave generation by velocity shear in collisionless plasmas. Journal of Plasma Physics 86:2.
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T. Alberti, G. Consolini & V. Carbone. (2019) A discrete dynamical system: The poor man’s magnetohydrodynamic (PMMHD) equations. Chaos: An Interdisciplinary Journal of Nonlinear Science 29:10.
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Francesco Valentini, Francesco Malara, Luca Sorriso-Valvo, Roberto Bruno & Leonardo Primavera. (2019) Building Up Solar-wind-like 3D Uniform-intensity Magnetic Fields. The Astrophysical Journal 881:1, pages L5.
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Leonardo Primavera, Francesco Malara, Sergio Servidio, Giuseppina Nigro & Pierluigi Veltri. (2019) Parametric Instability in Two-dimensional Alfvénic Turbulence. The Astrophysical Journal 880:2, pages 156.
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Tommaso Alberti, Giuseppe Consolini, Vincenzo Carbone, Emiliya Yordanova, Maria Marcucci & Paola De Michelis. (2019) Multifractal and Chaotic Properties of Solar Wind at MHD and Kinetic Domains: An Empirical Mode Decomposition Approach. Entropy 21:3, pages 320.
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Francesco Malara, Giuseppina Nigro, Francesco Valentini & Luca Sorriso-Valvo. (2019) Electron Heating by Kinetic Alfvén Waves in Coronal Loop Turbulence. The Astrophysical Journal 871:1, pages 66.
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Elisa De Giorgio, Sergio Servidio & Pierluigi Veltri. (2017) Coherent Structure Formation through nonlinear interactions in 2D Magnetohydrodynamic Turbulence. Scientific Reports 7:1.
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F. Valentini, C. L. Vásconez, O. Pezzi, S. Servidio, F. Malara & F. Pucci. (2017) Transition to kinetic turbulence at proton scales driven by large-amplitude kinetic Alfvén fluctuations. Astronomy & Astrophysics 599, pages A8.
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Francesco Malara, Francesca Di Mare, Giuseppina Nigro & Luca Sorriso-Valvo. (2016) Fast algorithm for a three-dimensional synthetic model of intermittent turbulence. Physical Review E 94:5.
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F. Pucci, C. L. Vásconez, O. Pezzi, S. Servidio, F. Valentini, W. H. Matthaeus & F. Malara. (2016) From Alfvén waves to kinetic Alfvén waves in an inhomogeneous equilibrium structure. Journal of Geophysical Research: Space Physics 121:2, pages 1024-1045.
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Roberto Bruno & Vincenzo CarboneRoberto Bruno & Vincenzo Carbone. 2016. Turbulence in the Solar Wind. Turbulence in the Solar Wind 43 98 .
C. L. Vásconez, F. Pucci, F. Valentini, S. Servidio, W. H. Matthaeus & F. Malara. (2015) KINETIC ALFVÉN WAVE GENERATION BY LARGE-SCALE PHASE MIXING. The Astrophysical Journal 815:1, pages 7.
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S. Oughton, W. H. Matthaeus, M. Wan & K. T. Osman. (2015) Anisotropy in solar wind plasma turbulence. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373:2041, pages 20140152.
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W. H. Matthaeus, S. Oughton, K. T. Osman, S. Servidio, M. Wan, S. P. Gary, M. A. Shay, F. Valentini, V. Roytershteyn, H. Karimabadi & S. C. Chapman. (2014) NONLINEAR AND LINEAR TIMESCALES NEAR KINETIC SCALES IN SOLAR WIND TURBULENCE. The Astrophysical Journal 790:2, pages 155.
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Franck Plunian, Rodion Stepanov & Peter Frick. (2013) Shell models of magnetohydrodynamic turbulence. Physics Reports 523:1, pages 1-60.
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P. Wu, S. Perri, K. Osman, M. Wan, W. H. Matthaeus, M. A. Shay, M. L. Goldstein, H. Karimabadi & S. Chapman. (2013) INTERMITTENT HEATING IN SOLAR WIND AND KINETIC SIMULATIONS. The Astrophysical Journal 763:2, pages L30.
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F. Malara. (2012) Alfvén waves in coronal holes: formation of discontinuities in inhomogeneous magnetic fields. Astronomy & Astrophysics 549, pages A54.
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W. H. Matthaeus, S. Servidio, P. Dmitruk, V. Carbone, S. Oughton, M. Wan & K. T. Osman. (2012) LOCAL ANISOTROPY, HIGHER ORDER STATISTICS, AND TURBULENCE SPECTRA. The Astrophysical Journal 750:2, pages 103.
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Minping Wan, Sean Oughton, Sergio Servidio & William H. Matthaeus. (2012) von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality. Journal of Fluid Mechanics 697, pages 296-315.
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S. Servidio, V. Carbone, P. Dmitruk & W. H. Matthaeus. (2011) Time decorrelation in isotropic magnetohydrodynamic turbulence. EPL (Europhysics Letters) 96:5, pages 55003.
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F. Carbone, A. Vecchio & L. Sorriso-Valvo. (2011) Spatio-temporal dynamics, patterns formation and turbulence in complex fluids due to electrohydrodynamics instabilities. The European Physical Journal E 34:8.
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Roland Grappin & Wolf-Christian Müller. (2010) Scaling and anisotropy in magnetohydrodynamic turbulence in a strong mean magnetic field. Physical Review E 82:2.
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L. Sorriso-Valvo, E. Yordanova & V. Carbone. (2010) On the scaling properties of anisotropy of interplanetary magnetic turbulent fluctuations. EPL (Europhysics Letters) 90:5, pages 59001.
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F. Valentini, F. Califano & P. Veltri. (2010) Two-Dimensional Kinetic Turbulence in the Solar Wind. Physical Review Letters 104:20.
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E. Lee, M. E. Brachet, A. Pouquet, P. D. Mininni & D. Rosenberg. (2010) Lack of universality in decaying magnetohydrodynamic turbulence. Physical Review E 81:1.
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V. Carbone, L. Sorriso-Valvo & R. Marino. (2009) On the turbulent energy cascade in anisotropic magnetohydrodynamic turbulence. EPL (Europhysics Letters) 88:2, pages 25001.
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W. H. Matthaeus, S. Oughton & Y. Zhou. (2009) Anisotropic magnetohydrodynamic spectral transfer in the diffusion approximation. Physical Review E 79:3.
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A. Shalchi, J. W. Bieber & W. H. Matthaeus. (2008) Pitch-angle scattering in pure two-dimensional and two-component turbulence. Astronomy & Astrophysics 483:2, pages 371-381.
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W.-C. Müller. 2009. Interdisciplinary Aspects of Turbulence. Interdisciplinary Aspects of Turbulence 223 254 .
M. Onofri, P. Veltri & F. Malara. (2007) Development and anisotropy of three-dimensional turbulence in a current sheet. Physics of Plasmas 14:6.
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Sebastien Galtier & Eric Buchlin. (2007) Multiscale Hall‐Magnetohydrodynamic Turbulence in the Solar Wind. The Astrophysical Journal 656:1, pages 560-566.
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L Sorriso-Valvo, V Carbone, R Bruno & P Veltri. (2006) Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind. Europhysics Letters (EPL) 75:5, pages 832-838.
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F. Reale, G. Nigro, F. Malara, G. Peres & P. Veltri. (2005) Modeling a Coronal Loop Heated by Magnetohydrodynamic Turbulence Nanoflares. The Astrophysical Journal 633:1, pages 489-498.
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S. Oughton, P. Dmitruk & W. H. Matthaeus. (2004) Reduced magnetohydrodynamics and parallel spectral transfer. Physics of Plasmas 11:5, pages 2214-2225.
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Wolf-Christian Müller, Dieter Biskamp & Roland Grappin. (2003) Statistical anisotropy of magnetohydrodynamic turbulence. Physical Review E 67:6.
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Sean Oughton, Pablo Dmitruk & William H. Matthaeus. 2003. Turbulence and Magnetic Fields in Astrophysics. Turbulence and Magnetic Fields in Astrophysics 28 55 .
S. Oughton, W. H. Matthaeus, P. Dmitruk, L. J. Milano, G. P. Zank & D. J. Mullan. (2001) A Reduced Magnetohydrodynamic Model of Coronal Heating in Open Magnetic Regions Driven by Reflected Low‐Frequency Alfven Waves. The Astrophysical Journal 551:1, pages 565-575.
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Pierluigi Veltri. (1999) MHD turbulence in the solar wind: self-similarity, intermittency and coherent structures. Plasma Physics and Controlled Fusion 41:3A, pages A787-A795.
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P. Pommois, P. Veltri & G. Zimbardo. (1999) Anomalous and Gaussian transport regimes in anisotropic three-dimensional magnetic turbulence. Physical Review E 59:2, pages 2244-2252.
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P. Veltri, F. Malara & L. Primavera. 1999. Nonlinear MHD Waves and Turbulence. Nonlinear MHD Waves and Turbulence 222 250 .
Sean Oughton, William H. Matthaeus & Sanjoy Ghosh. (1998) Scaling of spectral anisotropy with magnetic field strength in decaying magnetohydrodynamic turbulence. Physics of Plasmas 5:12, pages 4235-4242.
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P Giuliani & V Carbone. (1998) A note on shell models for MHD turbulence. Europhysics Letters (EPL) 43:5, pages 527-532.
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S. Oughton, K.-H. Rädler & W. Matthaeus. (1997) General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence. Physical Review E 56:3, pages 2875-2888.
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Sean Oughton. (2009) Ion parallel viscosity and anisotropy in MHD turbulence. Journal of Plasma Physics 56:3, pages 641-657.
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M. K. Verma, D. A. Roberts, M. L. Goldstein, S. Ghosh & W. T. Stribling. (1996) A numerical study of the nonlinear cascade of energy in magnetohydrodynamic turbulence. Journal of Geophysical Research: Space Physics 101:A10, pages 21619-21625.
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Francesco Malara, Leonardo Primavera & Pierluigi Veltri. (1996) Gompressive fluctuations generated by time evolution of Alfvénic perturbations in the solar wind current sheet. Journal of Geophysical Research: Space Physics 101:A10, pages 21597-21617.
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William H. Matthaeus, Sanjoy Ghosh, Sean Oughton & D. Aaron Roberts. (1996) Anisotropic three-dimensional MHD turbulence. Journal of Geophysical Research: Space Physics 101:A4, pages 7619-7629.
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Sean Oughton, William H. Matthaeus & Sanjoy Ghosh. 1996. Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence. Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence 273 279 .
Murshed Hossain, Perry C. Gray, Duane H. PontiusJr.Jr., William H. Matthaeus & Sean Oughton. (1995) Phenomenology for the decay of energy-containing eddies in homogeneous MHD turbulence. Physics of Fluids 7:11, pages 2886-2904.
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G. Zimbardo, P. Veltri, G. Basile & S. Principato. (1995) Anomalous diffusion and Lévy random walk of magnetic field lines in three dimensional turbulence. Physics of Plasmas 2:7, pages 2653-2663.
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V Carbone. (1995) Signed Measures in a Shell Model for Hydromagnetic Turbulence. Europhysics Letters (EPL) 29:5, pages 377-382.
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Vincenzo Carbone, Francesco Malara & Pierluigi Veltri. (1995) A model for the three-dimensional magnetic field correlation spectra of low-frequency solar wind fluctuations during Alfvénic periods. Journal of Geophysical Research 100:A2, pages 1763.
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V Carbone. (1994) Time Intermittency in a Shell Model for Fully Developed Hydromagnetic Turbulence. Europhysics Letters (EPL) 27:8, pages 581-586.
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P. Veltri. (1994) Low frequency turbulence and energy dissipation in the Solar Wind. Space Science Reviews 68:1-4, pages 63-74.
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A.Z Dolginov & M.E Katz. (1994) Interaction of cosmic rays with magnetohydrodynamical turbulence in cosmic media. Physics Reports 239:5-6, pages 285-364.
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P. Veltri. 1994. Fragmented Energy Release in Sun and Stars. Fragmented Energy Release in Sun and Stars 63 74 .
V. Carbone, P. Veltri & F. Malara. (1992) Anisotropy of magnetohydrodynamic Alfvénic fluctuations in the interplanetary space. Il Nuovo Cimento C 15:5, pages 621-630.
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P. Veltri, F. Malara & L. Primavera. 1992. Solar Wind Seven. Solar Wind Seven 559 564 .
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