In this course, we will go through the fundamental instability mechanisms of geophysical shear flows. We will begin with planar inviscid shear flows such as Couette and mixing layer flows and then reexamine them in 3D. Next, we will add the effect of stratification and explore the Taylor-Caulfield and Holmboe instabilities. The effect of rotation will introduce us to   inertial and symmetric instabilities as well as to baroclinic instability models such as the one of Eady and the quasi-geostrophic 2-layer model.  If time permits, we will look on the counter-intuitive effect of viscosity to destabilize shear flows in boundary layers via the Tolmein-Schlichting instability.

The focus throughout the course will be on the understanding of the physical mechanisms of these instabilities along rigorous mathematical derivations of their governing equations.