These are some derivations that I think are interesting, but are not included in the notes for my courses.  They are by no means groundbreaking, and not all are original.  Some are downright esoteric.

  • Virtual Temperature Approximation: Shows the rational behind a common approximation for virtual temperature using degrees Celsius and dimensional mixing ratio (g/kg).
  • Coriolis and Centrifugal Torques: Explores the torques from apparent forces on an object viewed in a rotating reference frame.
  • Running in the Rain: Discusses whether you will stay drier, or get wetter, by running versus walking to shelter when it is raining.
  • Mean Distance Between Drops: A derivation from probability theory to show the mean distance between cloud drops, rain droplets, or other aerosols.
  • Monty Hall Problem: A derivation from probability using Bayes’ Theorem to show an unintuitive result.
  • Vorticity and Absolute Angular Momentum:  Shows how the barotropic vorticity equation can be derived directly from the conseration of absolute angular momentum.