Eulerian Field vs LagrangianConceptual

[Saladsamurai]

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

 

[foxjwill]

I think what the text means is "specific" particle, i.e. one particular particle in the fluid. I agree, though, that fixed was a bad choice of word.

 

[Saladsamurai]

I think what the text means is "specific" particle, i.e. one particular particle in the fluid. I agree, though, that fixed was a bad choice of word.

Yes. I was assuming that by "fixed particle" they mean a "specific particle."

My problem is that they are referring to a "fixed particle" but they are also saying that this is the eulerian approach. But I thought that the fixed particle approach was lagrangian?

 

[Saladsamurai]

Any ideas on this one? I feel like I could move on, but I really want to understand what I am doing from here forward.

 

[foxjwill]

In the lagrangian frame of reference, the origin is always at the specific particle, while in the eulerian frame of reference, it is not.

 

[Saladsamurai]

In the lagrangian frame of reference, the origin is always at the specific particle, while in the eulerian frame of reference, it is not.

Yes. I am quite aware of that. But that is not my question. Please look at what I am asking.

The whole point of my question is that I KNOW that the eulerian frame stays fixed and watches different fluid particle entering and leaving. So why do they say

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 words in bold seem to contradict each other.