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## Eulerian Field vs Lagrangian::Conceptual

Okay. This is a very straight forward question. I believe that my text has an error or I am misunderstanding something.

It describes the Eulerian Field as:

 ...our coordinates are fixed in space and we observe a particle of fluid as it passes by-- as if we had scribed a set of coordinate lines on a glass window in a wind tunnel. This is the eulerian frame of reference as opposed to the lagrangian which follows the moving position of individual particles.
Then we go on to derive the acceleration field in this eulerian field by taking the Total Derivative of the Velocity Field vector, which yields:

$$\mathbf{a} = \frac{d\,\mathbf{V}}{d\,t} = \frac{\partial{V}}{\partial{t}} + (\mathbf{V}\cdot\nabla)\mathbf{V}$$

Okay great..I get all of that. Here is where I croak. It then summarizes what we just did by saying:

 We emphasize that this is the total time derivative that follows a particle of fixed identity, making it convenient for expressing laws of particle mechanics in the eulerian fluid field description. The operator d/dt is sometimes assigned a special symbol D/Dt to remind us that it contains four terms and follows a fixed particle.
This last quote keeps referring to "following a fixed particle" or "following a particle of fixed identity."

Isn't that by definition the Lagrangian frame? Or am I misinterpreting how they are using the word "following"?

Can someone clear up my confusion here?

Thank you,
Casey
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