## On the steady state of nonlinear quasiresonant Alfvén oscillations in one-dimensional magnetic cavity
^{1} Institute of Atomic and Molecular Physics, National
Research Council, Via Giardino 7, I-56127 Pisa, Italy^{2} School of Mathematical and Computational Sciences, St
Andrews University, St Andrews, Fife KY16 9SS, Scotland, UK^{3} On leave of Institute for Problems in Mechanics, Russian
Academy of Sciences, Vernadskii Prosp. 101, 117526 Moscow, Russia
We study the steady state of nonlinear, small-amplitude,
quasiresonant Alfvén oscillations in a homogeneous dissipative
hydromagnetic cavity which is forced by the shear motion of its
boundaries. It is shown that, even in the case of strong nonlinearity,
these oscillations can be represented, to leading order, by a sum of
two solutions in the form of oppositely propagating waves with
permanent shapes. An infinite set of nonlinear equations for the
Fourier coefficients of these solutions is derived which, in general,
admits multiple solutions, depending on the re-scaled total Reynolds
number,
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. Basic equations and assumptions
- 3. Derivation of the governing equations
- 4. Energetics
- 5. Multistability
- 5.1. One-mode approximation
- 5.2. Numerical results
- 6. Solutions with shocks
- 7. Conclusions
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: November 3, 1998 |