## Astrophysical

## Hydrodynamics

SYLLABUS

• Introduction on the astrophysical gas, ISM in particular

• Ideal fluids: Fluid approximation; Continuity and Euler equations; Equation of state: barotropic, adiabatic and isothermal flows; Energy equation; Heat sources: conduction and radiation; Entropy and heat equation; Propagation of sound waves, sound speed.

• Hydrostatic equilibrium: Isothermal sphere; X-ray emitting gas in galaxy clusters; Isothermal slab; Thickness of galaxy discs.

• Supersonic Flow: Mach number; Shock waves; Rankine-Hugoniot jump conditions; Entropy jump; Radiative shocks; Evolution of a supernova remnant.

• Hydrodynamic Instabilities: Convection, Kelvin-Helmholtz, Rayleigh Taylor, Gravitational and Thermal.

• Viscous fluids: Momentum flux and stress tensor; Viscous stress tensor; Navier-Stokes equation; Kelvin circulation theorem; Vorticity in viscous fluids; Energy dissipation in viscous flows; General heat equation.

• Turbulence: Reynolds number; Transition to turbulence in a Poiseuille flow; Fully developed turbulence, Kolmogorov law; Compressible turbulence, sources of turbulence in the ISM.

• Introduction to MHD: Charge neutrality, infinite conductivity; Field freezing; Euler equation with magnetic force; Magnetic Pressure and tension; Magnetic virial theorem; Hydromagnetic waves; Shocks with magnetic field.

Plan of the Lectures

Lecture 1 - Introduction on the ISM

Lecture 2 - Ideal fluids (basic concepts)

Lecture 3 - Ideal fluids (conservation equations)

Lecture 4 - Ideal fluids (conservation equations)

Lecture 5 - Sound waves and Hydrostatic equilibrium (slab, spherical systems)

Lecture 6 - Shock waves

Lecture 7 - Shock waves (continue)

Lecture 8 - Evolution of a supernova remnant

Lecture 9 - Instabilities (convection, Kelvin-Helmholtz, Rayleigh Taylor)

Lecture 10 - Instabilities (Gravitational and Thermal)

Lecture 11 - Viscous fluids (the stress tensor, Navier-Stokes equation)

Lecture 12 - Viscous fluids (Kelvin circulation theorem, energy dissipation)

Lecture 13 - Turbulence (Reynolds number, transition to)

Lecture 14 - Turbulence (Kolmogorov)

Lecture 15 - Magneto-hydrodynamics

Lecture 16 - Magneto-hydrodynamics (continue)