Waves and Instabilities in Rotating and Stratified Flows

This review intended primarily for Master degree students, presents the different types of classical waves that can occur in astro and geophysical flows. Inertial waves, caused by the rotation of the fluid, will first be introduced as well as their 2D version called Rossby waves. Then it will be shown how a density stratification of the fluid can make internal gravity waves appear. In each case and in the case where both rotation and stratification are present, the dispersion relations of the waves are derived. A differential rotation will then be added on the flow. The classical Rayleigh criterium for the centrifugal instability is recovered in the case of an homogeneous fluid but it will be shown that a new instability, called the strato-rotational instability (SRI), can occur when the fluid is stratified. Some experiments will be described. Finally, we will show how the application of a magnetic field can create Alfven waves in a rotating electrically conducting fluid and in which conditions the magneto-rotational instability (MRI) can grow.