What is the relationship between particle and energy frames in fluid dynamics?

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Discussion Overview

The discussion revolves around the relationship between particle and energy frames in fluid dynamics, specifically focusing on how to derive the particle frame 4-velocity from the energy-momentum tensor. The scope includes theoretical aspects of fluid dynamics and the implications of thermodynamic equilibrium.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about deriving the particle frame 4-velocity from the energy-momentum tensor, suggesting a potential connection to the energy frame.
  • Another participant proposes looking for a timelike eigenvector as a method to find the particle frame 4-velocity.
  • A subsequent post references a definition from Wikipedia regarding the stress-energy tensor in thermodynamic equilibrium, indicating that the fluid's four-velocity is an eigenvector in that context.
  • A participant questions the applicability of this approach for fluids out of equilibrium, expressing uncertainty about the necessary information beyond the stress-energy tensor.
  • One participant acknowledges a misunderstanding and admits to not knowing the answer for non-equilibrium conditions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the relationship between particle and energy frames, particularly in non-equilibrium situations. There is no consensus on how to approach the problem outside of equilibrium conditions.

Contextual Notes

The discussion highlights limitations in understanding the relationship between the particle frame and energy frame, especially when dealing with fluids that are not in thermodynamic equilibrium. There is an indication that additional information may be required to fully address the question.

bloby
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Hello.

Is there a way, as for the energy frame, to get the particle frame 4-velocity of a fluid from its energy-momentum tensor?
 
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Well, you could look for a timelike eigenvector.
 
Could you explain why?
 
Quoting Wikipedia: "For a fluid in thermodynamic equilibrium, the stress-energy tensor takes on a particularly simple form
Tαβ = (ρ + p/c2)uαuβ + p gαβ where uα is the fluid's four-velocity."

And clearly uα is an eigenvector.
 
Ok, but for a fluid out of equillibrium?
 
Sorry, I misunderstood. In that case I don't know the answer. Maybe you need to be given more information than just the stress-energy tensor.
 

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