Earth & Planetary Fluid dynamics

I taught this course along with Anand Gnanadesikan and we covered the fundamentals of fluid dynamics including conservation laws including those in the rotating frame, non-dimensional analysis, inertial and gravity waves. I had a ton of fun and I learned a lot. Below I have all the notes I prepared for my lectures. Some of the stuff was done live on the board, so they might be missing in there. But everything else, is right there. This post would be incomplete without writing out the basic equations:

$$\dfrac{\partial\rho}{\partial t} + \nabla\cdot\left(\rho\boldsymbol{u}\right) = 0$$ $$\rho\left(\dfrac{\partial\boldsymbol{u}}{\partial t} + \boldsymbol{u}\cdot\nabla\boldsymbol{u}\right) = -\nabla p - 2\rho\boldsymbol{\Omega}\times\boldsymbol{u} + \nabla\cdot\mathsf{S} + \boldsymbol{F} $$ $$\rho T \left(\dfrac{\partial s}{\partial t} + \boldsymbol{u}\cdot\nabla s\right) = \nabla\cdot(k\nabla T) + \Phi_\mu$$

Notes/Slides :

Conservation of mass and momentum

Rotating frame

Conservation of energy

Laminar flow

Boussinesq approximation

Rotating convection

Surface gravity waves

Inertial and gravity waves

Inertial and Rossby modes

Turbulence