Abstract
Transition to irregular behaviour of Magnetohydrodynamical (MHD) waves is investigated using a simple four-mode dynamical system worked out from the basic MHD equations by means of a Fourier and a multiple-scale analysis. In the initial stage of the transition, when most of the energy in concentrated in the low-wave-number Fourier component, the system behaves like a van dr Pol oscillator, exhibiting saddlenode bifurcations. Hopf bifurcations are found numerically when the low- and high-wavenumber components have comparable magnitude. Two Hopf bifurcations leading to a two-D torus are followed by bifurcation to a nonperiodic attractor.
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References
W.Mattig, A. Nesis: “Studies of Granular Velocities IV: Statistical Analysis of Granular Dopper Shifts”. Solar Phys. 36, 3–9 (1974).
J.V.Hollweg: “Coronal Heating by Waves” In Solar wind V, ed. by E.M.Naugebauer, NASA Conference Publication 2280, p. 5 (1983).
J.P.Eckmann: “Roads to Turbulence in Dissipative Dynamical Systems” Rev. Mod. Phys. 53, 643–668 (1981).
E.M.Lifshiftz, L.P.Pitaevskii: “Physical Kinetics” (Pergamon Press Oxford 1981 ).
L.Nocera, E.R.Priest: “Onset of an Energy cascade and Nonperiodic Behaviour in Nonlinear Propagation of MHD Waves” Submitted to Geophys. and Astrophys. Fluid Dynamics (1986). In press.
L.Nocera, E.R.Priest, J.V. Hollweg: “Nonlinear Development of Phase-mixed Alfvén Waves” Geophys. and Astrophys. Fluid Dynamics, 35, 111–129 (1986)
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© 1987 Springer-Verlag Berlin Heidelberg
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Nocera, L. (1987). Transition of Magnetohydrodynamical Waves in the Solar Atmosphere. In: Comte-Bellot, G., Mathieu, J. (eds) Advances in Turbulence. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83045-7_33
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DOI: https://doi.org/10.1007/978-3-642-83045-7_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83047-1
Online ISBN: 978-3-642-83045-7
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