Fluid Dynamics in Astrophysics and Cosmology

Fluid mechanics is a fundamental tool for the sciences of the Universe: from Earth and the giant planets to stars, accretion disks, and the interstellar medium, it is an essential approach for studying astrophysical objects. The course unit “Fluid Dynamics in Astrophysics and Cosmology” builds upon the “Hydrodynamics” course unit and is organized around 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 a stability analysis to an astrophysical problem

The overall objective of this course is to prepare students for the M2-level courses in stellar and interstellar astrophysics, which make extensive use of hydrodynamics and magnetohydrodynamics.

· Hydrodynamics

· Mathematical Tools

Terminal Control

1. Rotating Fluids

◦ equations and characteristic 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

◦ Review of the motion of charged particles in a magnetic field

◦ fluid approximation for describing 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 problem with the alternator

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

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