Abstract
This chapter presents Euler equation without and with the presence of a magnetic field. The equation is written in both spherical and cylindrical coordinates, and applied to a stellar envelope. Some examples involving the solar wind are given, and a discussion is presented on the escape velocity from stars. The chapter ends with some further examples applied to hot and cool stars.
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Bibliography
Apart from the references given in Chap. 1, in particular the books by Landau and Lifchitz (1971), Batchelor (1967), and Clarke and Carswell (2007), other texts can be used, as follows.
Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists. Academic, New York (2012) (New Edition of a Classic Book on Mathematical Methods of Physics)
Choudhuri, A. R.: The Physics of Fluids and Plasmas. Cambridge University Press, Cambridge (1998) Referred to in Chapter 1. Includes a good discussion of the Euler equation, especially in MHD
Castor, J.I., Abbott, D.C., Klein, R.I.: Astrophys. J. 195, 157 (1975) (Classic paper on Stellar Winds in Hot Stars, with a Discussion of the β Velocity Law. See Also Astrophys. J. Suppl. Ser. 139, 197 (1975))
Munson, B.R., Rothmayer, A.P., Okiishi, T.H., Huebsch, W.W.: Fundamentals of Fluid Mechanics. Wiley, New York (2012) (Introductory Text on Fluid Mechanics, Directed to Engineering Students, with Emphasis on the Fundamental Aspects of Fluid Flows, Including Eulerian and Lagrangian Descriptions)
Symon, K.R.: Mechanics. Addison-Wesley, Reading (1971) (Basic mechanics book, with a discussion on vectors and coordinates)
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Maciel, W.J. (2014). The Euler Equation. In: Hydrodynamics and Stellar Winds. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-04328-9_2
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DOI: https://doi.org/10.1007/978-3-319-04328-9_2
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