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.

- 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.

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