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:
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...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.
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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:
[tex]\mathbf{a} = \frac{d\,\mathbf{V}}{d\,t} = \frac{\partial{V}}{\partial{t}} + (\mathbf{V}\cdot\nabla)\mathbf{V}[/tex]
Okay great..I get all of that. Here is where I croak. It then summarizes what we just did by saying:
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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.
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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