Fluid dynamics in astrophysics and cosmology

Fluid mechanics is a fundamental tool for the sciences of the Universe: from Earth and giant planets to stars, accretion disks, and the interstellar medium, it is an essential approach for studying astrophysical objects. The "Fluid Dynamics in Astrophysics and Cosmology" course builds on the "Hydrodynamics" course, focusing on three central themes in astrophysics: rotating fluids, thermal convection, and magnetohydrodynamics.

· Be able to describe an astrophysical problem using fluid mechanics equations

· Understand the main properties of rotational flows, thermal convection, and magnetohydrodynamic flows.

· Know how to apply stability analysis to an astrophysical problem

The overall objective of this course is to enable students to tackle M2 courses in stellar astrophysics and interstellar media, which make extensive use of hydrodynamics and magnetohydrodynamics.

· Hydrodynamics

· Math Tools

Terminal control

1. Rotating fluids

◦ characteristic equations and numbers

◦ geostrophic flow

◦ Inertial waves and Rossby waves

◦ effects of viscosity

2. Thermal convection

◦ conductive balance

◦ Boussinesq approximation and inelastic approximation

◦ baroclinicity

◦ Schwarzschild criterion and Rayleigh-Bénard instability

◦ Ledoux criterion and thermohaline convection

3. Magnetohydrodynamics

◦ reminders about the movement of charged particles in a magnetic field

◦ Fluid approximation for the description of plasmas and equations of motion

◦ remarkable properties of MHD flows

◦ frozen field, magnetic pressure and tension, force-free field, equipartition

◦ Alfvén waves and magnetosonic waves

◦ the dynamo problem

· An Introduction to Fluid Dynamics, M. Rieutord, De Boeck, 2014

· Astrophysics for Physicists, A.R. Choudhuri, Cambridge University Press, 2010