Meromorphy and topology of localized solutions in the Thomas–MHD model

Article English OPEN
Fournier, Jean-Daniel ; Galtier, S. (2001)

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.
  • References (48)
    48 references, page 1 of 5

    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.

  • Similar Research Results (1)
  • Metrics
    views in OpenAIRE
    views in local repository
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    Warwick Research Archives Portal Repository - IRUS-UK 0 22
Share - Bookmark