So I'm a high school student with some free time on my hands and I've been trying to learn about the Navier-Stokes equation. Anyway, this set of lecture notes from UCLA is a bit hard to understand. Wether due to poor wording or me being unfamiliar with the notation, a paraphrase of this section would be beneficial to me!
Screenshot of the section in question
So I understand that omega represents the region the fluid occupies in two or three dimensional space. And I understand the differences between "x" and "X" as well as the concepts of Eularian coordinates and Lagrangian coordinates. But the next part is a bit tricky.
I have no idea what the phi function is supposed to indicate. The author claims it "describes the change in the particles position." But then goes on to define the function in a cryptic manner. I understand the technical notation...but not really sure what they are getting at. In particular...what does "W" represent. And why is it interchangeable with "X" in the function definition?
If anyone could paraphrase this section such that it is more clear / easier to understand for me that would be great! Particularly just about what the phi function takes in as arguments, and what it returns!
Honestly I'm just curious about this sort of stuff but have little to no experience as you can tell :)