Introduction on the astrophysical gas, ISM in particular

__: 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.__

Ideal fluids

Ideal fluids

__Hydrostatic equilibrium__: Isothermal sphere; X-ray 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.

__Hydrodynamical Instabilities__: preliminaries: Archimedes and Bernoulli; Convection, Kelvin-Helmholtz, Rayleigh Taylor, Gravitational, Rotational, 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.

(if there is time) Basics of hydrodynamic simulations and/or observations of ISM.