Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Fournier, Jean-Daniel; Galtier, S. (2001)
Publisher: Cambridge University Press
Languages: English
Types: Article
Subjects: QA
The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Brunelli, J. C. and Das, A. 1997 A Lax description for polytropic gas dynamics. Phys. Lett. A 235A, 597{602.
    • Burgers, J. M. 1939 Mathematical examples illustrating relations occurring in the theory of turbulent uid motion. Kon. Ned. Akad. Wet. Verh. 17, 1{53.
    • Burgers, J. M. 1974 The Nonlinear Diffusion Equation. Dordrecht: Reidel.
    • Burlaga, L. F. 1991 Intermittent turbulence in the solar wind. J. Geophys. Res. 96, 5847{5851.
    • Chabat, B. 1990 Introduction a l'Analyse Complexe. Moscow: Mir.
    • Cole, J. 1951 On a quasi-linear parabolic equation occurring in aerodynamics. Q. Appl. Maths 9, 225{236.
    • Conte, R. and Boccara, N. (eds) 1990 Partially Integrable Evolution Equations in Physics. Dordrecht: Kluwer.
    • Dobrowolny, M., Mangeney, A. and Veltri, P. 1980 Properties of magnetohydrodynamic turbulence in the solar wind. Astron. Astrophys. 83, 26{32.
    • Festou, M. C., Rickman, H. and West, R. M. 1993 Comets. Astron. Astrophys. Rev. Part I 4, 363{447.
    • Flaschka, H., Newell, A. C. and Tabor, M. 1991 Integrability, What is integrability? In: Nonlinear Dynamics (ed. V. E. Zakharov). Berlin: Springer-Verlag, pp. 73{114.
    • Fournier, J.-D. 1986 Proprietes locales et singularites complexes en dynamique non linea re. In: Methodes Mathematiques pour l'Astrophysique (ed. M. Auvergue and A. Baglin). Nice: SFSA, pp. 333{383 (available from Dr D. Benest, Observatoire de Nice).
    • Fournier, J.-D. and Bessis, D. 1994 Dealing with the singularities of analytic functions. In: An Introduction to Methods of Complex Analysis and Geometry for Classical Mechanics and Non-Linear Waves (ed. D. Benest and C. Froesuhle). Gif sur Yvette: Editions Frontieres, pp. 1{45.
    • Fournier, J.-D. and Frisch, U. 1983 L'equation de Burgers deterministe et statistique. J. Mec. Theor. Appl. 2, 699{750.
    • Fournier, J.-D., Levine, G. and Tabor, M. 1988 Singularity clustering in the Duf ng oscillator. J. Phys. A21, 33{54.
    • Fournier, J.-D., Spiegel, E. A. and Thual, O. 1989 Meromorphic integrals of two nonintegrable systems. In: Non Linear Dynamics (ed. G. Turchetti). Singapore: World Scienti c, pp. 366{373.
    • Frisch, U. and Morf, R. 1981 Intermittency in nonlinear dynamics and singularities at complex times. Phys. Rev. A23, 2673{2705.
    • Galsgaard, K. and Nordlund, A. 1996 The heating and activity of the solar corona: boundary shearing of an initially homogeneous magnetic eld. J. Geophys. Res. 101, 13445{13460.
    • Galtier, S. and Fournier, J.-D. 1998 Shocks and antishocks in the MHD{Thomas model. In: Nonlinear Dynamics in the Heliosphere. Geophysical Research Abstracts (III), EGS Conference, Nice.
    • Galtier, S. and Pouquet, A. 1998 Solar are statistics with a one-dimensional MHD model. Solar Phys. 179, 141{165.
    • Galtier, S., Nazarenko, S. V., Newell, A. C. and Pouquet, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447{488.
    • Goldstein, M. L. and Roberts, D. A. 1999 Magnetohydrodynamic turbulence in the solar wind. Phys. Plasmas 6, 4154{4160.
    • Gurbatov, S. N., Simdyankin, S. I., Aurell, E., Frisch, U. and Toth, G. 1997 On the decay of Burgers turbulence. J. Fluid Mech. 344, 339-374.
    • Heiles, C., Goodman, A. A., McKee, C. F. and Zweibel, E. G. 1993 Magnetic elds in starforming regions : observations. In: Protostars and Planets III (ed. E. H. Levy, J. I. Lunine, M. Guerrieri and M. S. Matthews). Tucson: University of Arizona Press, pp. 279{326.
    • Hopf, E. 1950 The partial differential equation ut + uux = uxx. Commun. Pure Appl. Mech. 3, 201{230.
    • Kida, S. 1979 Asymptotic properties of Burgers turbulence. J. Fluid Mech. 93, 337{377.
    • Levine, G. and Tabor, M. 1988 Integrating the nonintegrable: analytic structure of the Lorenz system revisited. Physica D33, 189{210.
    • Marsch, E. and Tu, C. Y. 1994 Non-Gaussian probability distributions of solar wind uctuations. Ann. Geophys. 12, 1127{1138.
    • Newell, A. C. 1985 Solitons in Mathematics and Physics. Philadelphia: SIAM.
    • Ng, C. S. and Bhattacharjee, A. 1997 Scaling of anisotropic spectra due to the weak interaction of shear-Alfven wave packets. Phys. Plasmas 4, 605{610.
    • Olver, P. J. and Nutku, Y. 1988 Hamiltonian structures for systems of hyperbolic conservation laws. J. Math. Phys. 29, 1610{1619.
    • Parker, E. N. 1994 Spontaneous Current Sheets in Magnetic Fields. Oxford University Press.
    • Passot, T. 1986 Le test de Painleve. In: Methodes Mathematiques pour l'Astrophysique. (ed. M. Auvergne and A. Baglin). Nice: SFSA, pp. 161{170 (available from Dr D. Benest, Observatoire de Nice).
    • Passot, T. 1987 Simulations numeriques d'ecoulements compressibles. PhD Thesis, Universite de Nice.
    • Passot, T. and Pouquet, A. 1986 The Painleve analysis on the Burgers' MHD. Phys. Lett. 118, 121{123.
    • Passot, T. and Vazquez-Semadeni, E. 1998 Density probability distribution in onedimensional polytropic gas dynamics. Phys. Rev. E58, 4501{4510.
    • Pouquet, A., Galtier, S. and Politano, H. 1999 Mechanisms of injection and dissipation of energy and their relation to the dynamics of the interstellar medium. In: New Perspectives on the Interstellar Medium. (ed. A.R. Taylor, T.L. Landecker and G. Joncas). ASP Conference Series, Vol. 168, pp. 417{426.
    • Priest, E. R. 1982 Solar Magnetohydrodynamics. Dordrecht: Reidel.
    • Schwenn, R. and Marsch, E. 1991 Physics of the Inner Heliosphere II: Particles, Waves and Turbulence. Berlin: Springer-Verlag.
    • Shebalin, J. V., Matthaeus, W. H. and Montgomery, D. 1983 Anisotropy in MHD turbulence due to a mean magnetic eld. J. Plasma Phys. 29, 525{547.
    • Sulem, C., Fournier, J.-D., Frisch, U. and Sulem, P. L. 1979 Remarques sur un modele unidimensionnel pour la turbulence magnetohydrodynamique. C. R. Acad. Sci. Paris 288, 571{573.
    • Sulem, C., Sulem, P. L. and Frisch, H. 1983 Tracing complex singularities with spectral methods. J. Comput. Phys. 50, 138{161.
    • Taylor, J. B. 1986 Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58, 741{763.
    • Thomas, J. H. 1968 Numerical experiments on a model system for magnetohydrodynamic turbulence. Phys. Fluids 11, 1245{1250.
    • Thomas, J. H. 1970 Model equations for magnetohydrodynamic turbulence. A gas dynamics analogy. Phys. Fluids 13, 1877{1879.
    • Weiss, J., Tabor, M. and Carnevale, G. 1983 The Painleve property for partial differential equations. J. Math. Phys. 24, 522{526.
    • Wild, N., Gekelman, W. and Stenzel, R. L. 1981 Resistivity and energy ow in a plasma undergoing magnetic eld line reconnection. Phys. Rev. Lett. 46, 339{342.
    • Zank, G. P. and Matthaeus, W. H. 1992 The equations of reduced magnetohydrodynamics. J. Plasma Phys. 48, 85{100.
    • Zilbersher, D., Gedalin, M., Newbury, J. A. and Russell C. T. 1998 Direct numerical testing of stationary shock model with low Mach number shock observations. J. Geophys. Res. 103, 26775.
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

Share - Bookmark

Cite this article