Eulerian Field vs LagrangianConceptual

  1. Saladsamurai

    Saladsamurai 3,016
    Gold Member

    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:

    [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:

    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. jcsd
  3. 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.
     
  4. Saladsamurai

    Saladsamurai 3,016
    Gold Member

    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?
     
  5. Saladsamurai

    Saladsamurai 3,016
    Gold Member

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

    Saladsamurai 3,016
    Gold Member

    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

    The words in bold seem to contradict each other.
     
    Last edited: Oct 25, 2009
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?