Transition of Magnetohydrodynamical Waves in the Solar Atmosphere
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.
KeywordsHopf Bifurcation Alfven Wave Coronal Heating Convective Layer Magnetohydrodynamical Wave
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- 2.J.V.Hollweg: “Coronal Heating by Waves” In Solar wind V, ed. by E.M.Naugebauer, NASA Conference Publication 2280, p. 5 (1983).Google Scholar
- 4.E.M.Lifshiftz, L.P.Pitaevskii: “Physical Kinetics” (Pergamon Press Oxford 1981 ).Google Scholar
- 5.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.Google Scholar