# New PDF release: Astrophysical Flows

By James E. Pringle, Andrew King

Just about all traditional topic within the Universe is fluid, and fluid dynamics performs a very important function in astrophysics. This new graduate textbook offers a simple figuring out of the fluid dynamical procedures appropriate to astrophysics. the math used to explain those procedures is simplified to convey out the underlying physics. The authors disguise many themes, together with wave propagation, shocks, round flows, stellar oscillations, the instabilities as a result of results equivalent to magnetic fields, thermal riding, gravity, shear flows, and the elemental ideas of compressible fluid dynamics and magnetohydrodynamics. The authors are administrators of the united kingdom Astrophysical Fluids Facility (UKAFF) on the college of Leicester, and editors of the Cambridge Astrophysics sequence. This e-book has been built from a direction in astrophysical fluid dynamics taught on the college of Cambridge. it's appropriate for graduate scholars in astrophysics, physics and utilized arithmetic, and calls for just a simple familiarity with fluid dynamics.

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**Extra resources for Astrophysical Flows**

**Example text**

3 Waves in a magnetic medium We have seen that information travels through a compressible medium at the local sound speed. If the medium also has a magnetic field there are other ways of communicating physical information through it. We consider the same unperturbed fluid as before, with uniform density ρ0 , uniform pressure p0 and zero velocity u0 , and add a uniform magnetic field B0 . e. ρ = ρ0 + ρ , p = p0 + p and small velocity u) and now have to add the perturbation to the magnetic field in the form |B0 |.

The derivation of waves in magnetic media given here follows that given in Jackson (1998, Chap. 7); an alternative description is given by Sturrock (1994, Chap. 14). Non-linear flow of a compressible fluid in one dimension, the concept of characteristics and the development and treatment of shocks are discussed further in Zel’dovich & Raizer (1967, Chap. I) and in Landau & Lifshitz (1959, Chaps. IX, X). An analogy with traffic flow is described in Witham (1974, Chap. 3) and in Billingham & King (2000, Chap.

For a simple example of how shocks arise we consider a long tube of compressible fluid (for example a gas) lying along the positive x-axis, with one end at x = 0. We assume that the gas flow is one-dimensional, and that initially the fluid is at rest, with u = 0 and cs = c0 = constant. At time t = 0 we start to move a piston into the fluid from the end at x = 0. We assume that the piston moves at constant acceleration a, so that, as shown in Fig. 4 at time t > 0, the piston is at position xp (t) = 12 at 2 and has velocity x˙ p (t) = at.