By James E. Pringle, Andrew King
Just about all traditional subject within the Universe is fluid, and fluid dynamics performs a very important position in astrophysics. This new graduate textbook offers a uncomplicated realizing of the fluid dynamical methods appropriate to astrophysics. the math used to explain those techniques is simplified to carry out the underlying physics. The authors conceal many issues, together with wave propagation, shocks, round flows, stellar oscillations, the instabilities as a result of results resembling magnetic fields, thermal using, gravity, shear flows, and the fundamental suggestions 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 booklet has been constructed from a direction in astrophysical fluid dynamics taught on the collage of Cambridge. it really is compatible for graduate scholars in astrophysics, physics and utilized arithmetic, and calls for just a simple familiarity with fluid dynamics.
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Extra info for Astrophysical Flows
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. 7). 1 Consider waves in a uniform compressible medium with uniform magnetic field B and sound speed cs . 91) where (ux , uy , uz ) is a constant vector. 92) and find two similar equations for uy and uz . If ux = 0, show that the form of the motion is an incompressible (Alfvén) wave with phase velocity VA cos θ. 93) where = ω/(kVA ) is the dimensionless phase velocity and β = cs /VA is a dimensionless measure of the strength of the field.
Deduce that (us − U+ )(us + U− ) = −γ ps /ρs . 114) Similarly apply eq. 113) to both the pre- and post-rebound configurations and hence, using eq. 114), obtain the following relationship: 2γ γ +1 2 = In the case of a strong shock (p0 p0 γ −1 + ps γ +1 p1 γ −1 . 115) ps ), show that 3γ − 1 p1 = . 7 At time t = 0, an infinite tube contains gas with uniform density and sound speed c0 in the range x > 0 and has a stationary piston at x = 0. For t > 0 the piston moves subsonically with constant velocity −U , where U > 0.
We also assume that the flow is isentropic (the details of the flow are qualitatively similar for other choices of the relation between p and ρ). The isentropic assumption implies that throughout the flow p = Kρ γ for some constant K and DS/Dt = 0. We take the magnetic field to be zero. 42) Dt cs Dt where the sound speed is given by cs2 = γ p/ρ. Eliminating Dρ/Dt from these two equations, we obtain 1 ∂p u ∂p ∂u + + cs = 0. 43) ρcs ∂t ρcs ∂x ∂x The momentum equation is given by ∂u ∂u 1 ∂p +u + = 0.
Astrophysical Flows by James E. Pringle, Andrew King