Tutorial - Fourier Space Representation-2 — Lesson 6

This lesson covers the concept of non-linear interactions in physics, particularly in the context of velocity fields. The instructor provides detailed explanations and examples to illustrate how different modes interact with each other and how their amplitudes can change over time. The lesson also introduces the concept of Fourier modes and how they can be used to visualize these interactions. The instructor further explains how to derive equations for the evolution of these amplitudes and how to solve them. The lesson concludes with a discussion on the physical implications of these interactions, using the example of 3D convection velocity fields.

Video Highlights

00:55 - Explanation of Fourier modes and their interaction
03:52 - Discussion on the computation of pressure term
05:42 - Explanation of the convolution in the non-linear term
09:11 - Discussion on the computation of A dot, B dot, and C dot
15:19 - Explanation of the Craya-Herring basis to eliminate pressure term
18:04 - Explanation of the physical example of 3D convection velocity field
23:32 - Discussion on the oscillation of A, B, C in the absence of viscosity

Key Takeaways

- Non-linear interactions occur when different modes interact with each other, causing their amplitudes to change over time.
- Fourier modes provide a useful tool for visualizing these interactions.
- Equations for the evolution of these amplitudes can be derived and solved, providing insights into the dynamics of these interactions.
- The concept of non-linear interactions has significant implications in physics, particularly in the context of 3D convection velocity fields.