# Eulerian Field vs LagrangianConceptual

1. Oct 24, 2009

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:

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:

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

2. Oct 25, 2009

### 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.

3. Oct 25, 2009

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?

4. Oct 25, 2009

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.

5. Oct 25, 2009

### 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.

6. Oct 25, 2009