Abstract
As mentioned in Sect. 11.3, magnetic fields have tension. Hence, it will be easily supposed that when a line of force is shaked, a perturbation is transported along the line. This is really shown by Alfvén, and the wave is called the Alfvén wave. The pure Alfvén wave is a transverse wave. However, fluids are compressible gases and pressure perturbations can coexist. Hence, in general situations wavy perturbations can have both characteristics of transverse and longitudinal waves. In this chapter we describe basic characteristics of MHD waves in homogeneous MHD fluids. MHD shock waves are also described.
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Notes
- 1.
In this section the flow speed u 1 is normalized by Alfvén speed, not by acoustic speed, different from the case of fluid shocks in Sect. 4.6.
- 2.
When the gas passes through the shock, its entropy can only increase. In the case of weak MHD shocks, it is shown that the entropy increase implies s > 1 (e.g., Landau and Lifshitz 1960). They say that this result seems to hold for shock waves of any intensity.
- 3.
\(\mathcal {M}_{\mathrm {A}}^2\) corresponds to \(\omega ^2/k^2 c_{\mathrm {A}}^2\) and cos2 θ 1 to \(k_z^2/k^2\).
References
Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media. Pergamon Press, Oxford (1960)
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Kato, S., Fukue, J. (2020). Waves and Shocks in Magnetohydrodynamical Fluids. In: Fundamentals of Astrophysical Fluid Dynamics. Astronomy and Astrophysics Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-4174-2_13
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DOI: https://doi.org/10.1007/978-981-15-4174-2_13
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