By James E. Pringle, Andrew King

Just about all traditional topic within the Universe is fluid, and fluid dynamics performs a vital function in astrophysics. This new graduate textbook presents a simple knowing of the fluid dynamical techniques suitable to astrophysics. the maths used to explain those procedures is simplified to deliver out the underlying physics. The authors disguise many themes, together with wave propagation, shocks, round flows, stellar oscillations, the instabilities attributable to results corresponding to magnetic fields, thermal riding, gravity, shear flows, and the elemental techniques of compressible fluid dynamics and magnetohydrodynamics. The authors are administrators of the united kingdom Astrophysical Fluids Facility (UKAFF) on the collage of Leicester, and editors of the Cambridge Astrophysics sequence. This e-book has been constructed from a path 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 uncomplicated familiarity with fluid dynamics.

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78) where This implies 1 ρ e + u 2 + p ux 2 2 = 0. 79) 1 Again, making use of eq. 69), this implies 1 2 p u +e+ 2 ρ 2 = 0. 80) 1 The three eqs. 80) are known as the Rankine–Hugoniot equations. 3 show that we can turn these into expressions for the velocity and density jumps (u2 /u1 ), (ρ2 /ρ2 ) in terms of the (upstream) Mach number M = u1 /cs of the shock. Physically what happens in a shock is that kinetic energy is turned into heat energy by dissipation. 4 shows this explicitly, and we find that the entropy of the fluid is higher on the downstream side of the shock.

This curve describes the motion of something which moves at speed dφ/dt along the x-axis (see Fig. 2). Then the time derivative of f (x, t) as seen by this something is given by df dt φ = dφ ∂f ∂f + . 52) = u + cs , dt 28 Compressible media t x = (t) x Fig. 2. Path of a point moving with speed dφ/dt along the x-axis. eq. 53) dt and thus that J+ = constant. 54) eq. 55) dt and thus that J− = constant. The curves C+ and C− are known as characteristic curves, or simply characteristics. 56) γ −1 and 2cs J− = u − .

24) with respect to time, and use eqs. 26) to eliminate ∂ρ /∂t and ∂b/∂t to obtain a linear equation for the velocity perturbation u: ρ0 ∂ 2u = cs2 ∇{ρ0 div u} − B0 ∧ {∇ ∧ [∇ ∧ (u ∧ B0 )]}. 29) which we shall call the vectorial Alfvén velocity . Then the equation becomes ∂ 2u − cs2 ∇(div u) + VA ∧ {∇ ∧ [∇ ∧ (u ∧ VA )]} = 0. 30) ∂t 2 Since each term contains either two time derivatives or two space derivatives, this is clearly a wave equation of some sort. e. B0 = VA = 0) then the equation reduces to the equation for simple acoustic waves that we had before.