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

In summary, the conversation discusses the possibility of obtaining a fluid's particle frame 4-velocity from its energy-momentum tensor, particularly in thermodynamic equilibrium where the stress-energy tensor takes on a simple form. It is suggested to look for a timelike eigenvector, which would be the fluid's four-velocity. However, for a fluid out of equilibrium, more information may be needed to determine the particle frame 4-velocity.
  • #1
bloby
112
8
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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  • #2
Well, you could look for a timelike eigenvector.
 
  • #3
Could you explain why?
 
  • #4
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.
 
  • #5
Ok, but for a fluid out of equillibrium?
 
  • #6
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.
 

1. What is the difference between particle and energy frames?

Particle and energy frames refer to two different ways of understanding and describing physical phenomena. Particle frames focus on the behavior and properties of individual particles, whereas energy frames focus on the flow and transfer of energy between particles.

2. How are particle frames and energy frames related?

Particle and energy frames are related in that they both provide different perspectives on the same physical system. While particle frames describe the behavior of individual particles, energy frames provide a more macroscopic view of how energy is transferred and transformed between particles.

3. What are some examples of particle frames?

Particle frames are commonly used in fields such as particle physics, where the behavior and interactions of subatomic particles are of interest. They are also used in chemistry to describe the properties and behavior of atoms and molecules.

4. How are energy frames used in everyday life?

Energy frames are used in everyday life to understand and describe various phenomena, such as the transfer of heat and the flow of electricity. They are also used in fields such as engineering and thermodynamics to analyze and design systems that involve the transfer and conversion of energy.

5. Can particle and energy frames be used together?

Yes, particle and energy frames are often used together to provide a more comprehensive understanding of physical systems. For example, in the field of quantum mechanics, both particle and energy frames are used to describe the behavior of particles on a microscopic scale.

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