Rotating Convection Instabilities — Lesson 3

This lesson covers the concept of rotating convection instability, focusing on the Navier-Stokes equation and the addition of the Coriolis force. The lesson explains how the Coriolis force affects the velocity field and the role of non-dimensionalization in the equation. It also introduces the Taylor and Ekman numbers, which are related to rotation. The lesson further discusses the importance of non-dimensional numbers like the Rayleigh number and the Taylor number in determining instability conditions. The lesson concludes with an exploration of eigenvalues and eigenvectors in the context of instability.

Video Highlights

00:33 - Explanation of Navier-Stokes equation and the addition of the coriolis force
01:02 - Explanation of the coriolis force and its non-dimensionalization
03:47 - Discussion on the concept of Rayleigh critical
08:40 - Introduction to the concept of inertial waves
10:02 - Explanation of the process of finding neutral stability
11:12 - Discussion on the concept of Rayleigh critical at a given Taylor number

Key Takeaways

- The Navier-Stokes equation for rotating convection includes an additional term for the Coriolis force.
- Non-dimensionalization is crucial in the equation, particularly for the Coriolis force.
- The Taylor and Ekman numbers, related to rotation, are introduced.
- Non-dimensional numbers like the Rayleigh number and the Taylor number are key in determining instability conditions.
- Eigenvalues and eigenvectors play a significant role in understanding instability.