Astrophysical Fluid Dynamics

The course aims at providing theoretical knowledge concerning astrophysical fluid dynamics. The course will consider the fluid equations, discussing astrophysically relevant equilibrium configurations (such as polytropic spheres), wave phenomena, shocks and instabilities, such as the gravitational instability. In the second part of the course, the focus will be on accretion discs and their applications in astrophysics.

At the end of the course, the student will be able to: 1. Describe and solve fluid equations in specific configurations. 2. Recognize and describe hydrostatic equilibrium configurations in astrophysical contexts. 3. Derive the dispersion relation for the propagation of sound waves and dispersive waves. 4. Solve the equations describing shock waves. 5. Recognize the fluid processes at work in the dynamics of astronomical objects, such as stars, the interstellar medium and gas around compact objects. 6. Describe the Navier-Stokes equations and the role of viscosity in astrophysics and in physics, with special attention to turbulence. 6. Describe the equations that determine the evolution of accretion discs. 7. Recognize the spectrum of an accretion disc and derive its physical properties. 8. Understand the dynamics and emission from accretion discs in specific contexts, such as compact objects and young stars.