Quantization and fluid mechanics?

In summary: They investigated the so-called "Hirschfelder modes" of a fluid, which are normal modes that are stable under minimal perturbations. I don't think this is the best way to approach the problem, as it seems to involve a decomposition of the dynamics that doesn't seem to work for systems with significant perturbations.
  • #1
quantumfireball
91
0
Quantization and fluid mechanics??

Cant quantum field theory be applied to releativistic imcompressible fluids?
cant the velocity vector field be quantized?
will the pressure of the fluid play the role of the 4th component of the four vector?
what would be the corresponding quanta?
(I know this might sound extremely stupid
but ......)
 
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  • #2
I don't know about this, but I must ask that is there Lagrangian formulation available for the Navier-Stokes system? If there is, then it could be possible to proceed with somewhat similar techniques as with the other quantum fields too.
 
  • #3
quantumfireball said:
will the pressure of the fluid play the role of the 4th component of the four vector?

You would probably need to deal with the stress-energy tensor, which is a 2nd-rank tensor, instead of with some four component object.
 
  • #4
i didnt know it would be so complicated
has anyone written a paper on this?
please elaborate on why to use a tensor?
 
  • #5
relativistic hydrodynamics of well known. so is quantizing density fluctuations of a fluid. one proceeds in the usual way by reducing the system to normal modes and quantizing those. I guess the relativistic quantum fluid is a bit harder, but there seem to be a few papers on it.

also, people use relativistic hydrodynamics to simulate nuclear collisions at the relativistic heavy ion collider with some degree of success.
 
  • #6
olgranpappy said:
relativistic hydrodynamics of well known. so is quantizing density fluctuations of a fluid. one proceeds in the usual way by reducing the system to normal modes and quantizing those. I guess the relativistic quantum fluid is a bit harder, but there seem to be a few papers on it.

also, people use relativistic hydrodynamics to simulate nuclear collisions at the relativistic heavy ion collider with some degree of success.

What are normal modes with fluids?
 
  • #7
I think guys that the problem (the worst one) is that our equations display a non linear dynamics----> all our theories about normal modes fail... we can't use such a decomposition... i think that works only for small perturbation of the fields involved...
regards;
marco;
 
  • #8


In this regard, consider the work of Joseph Hirschfelder et al circa 197Os.
 

1. What is quantization in fluid mechanics?

Quantization in fluid mechanics refers to the process of discretizing or breaking down a continuous fluid into discrete units or particles. This is often done to simplify complex fluid dynamics equations and make them more manageable for analysis and prediction.

2. How does quantization affect fluid flow?

Quantization can have a significant impact on fluid flow, as it introduces randomness and uncertainty into the behavior of fluids. In some cases, quantization can lead to turbulence and chaotic flow patterns, while in others it can lead to more predictable behavior.

3. What is the role of quantization in turbulence?

Quantization plays a crucial role in turbulence, as it can lead to the formation of vortices and other chaotic structures within fluids. These vortices can have a significant impact on the transport of momentum and energy within the fluid, making turbulence a complex and challenging phenomenon to study.

4. What are some applications of quantization in fluid mechanics?

Quantization has numerous applications in fluid mechanics, including in the study of turbulent flows, the development of numerical models for predicting fluid behavior, and in the design of efficient fluid systems. It is also essential in fields such as aerodynamics, hydrodynamics, and oceanography.

5. How is quantization related to the concept of fluid density?

The concept of quantization is closely related to fluid density, as the quantized particles within a fluid have a specific mass and volume. This allows for the calculation of fluid density, which is a crucial parameter in understanding the behavior of fluids and their interactions with other objects.

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