The existence of turbulence in astrophysical fluids has been living as a well-known unsolved problem for a couple of decades. The range transitions among three distinct scales of the micro-fluidic kinetics are still lying obscure. In this context, is there any equation of state to describe turbulent fluid media in the fabric of the modified (by turbulence) macroscopic Navier-Stokes equation?
Not sure about, what do you mean for "modified macroscopic" ,the equations for the relativistic case?
Dear Prof Filippo-Maria-Denaro:
Thanks a lot for your response. As clearly written above, it simply means the "macroscopic fluid state that is modified by turbulence". Even more clearly, could do you modify your conventional equation of state to describe turbulent fluids? If yes or no, how?
Warm regards,
PK Karmakar
P.K. Karmakar
If you consider non-relativistic flows, it is largely accepted that turbulence is not a change in the microscopic state of fluid and the standard NSE are an acceptable model (even if with some limits). I agree with this model because turbulence is a regime that is also transitional and laminar, depending on the characteristic scale chosen by the observer.
Nevethless, I read also different proposals about a change in the state. You can find some posts here on RG.
Dear Professor Karmakar
Can you please explain which conventional equations are you talking about for turbulent fluids?. Is there any equation available for turbulent fluids?
It is exactly what I am interested in. I do not work on turbulence, but willing to work.
I would like to know how you handle fluid turbulence mathematically.
How do you modify the fluid momentum equation for turbulence to work sensibly?
Does there exist any equation of state modified in the presence of turbulence?
I personally work using the standard NSE model. From that you can derive some formulations based on local filtering (LES) or on statistical mean (RANS).
But no changes in the basic state equations, only additional model relations to close the unresolved terms.
Dear Prof Filippo-Maria-Denaro:
Thanks a lot for your useful reply again and active cooperation. It would be nicer to see some worthful references as per your valuable suggestions.
Warm regards,
Pralay Kumar Karmakar
There are many many references... I can suggest some useful and modern textbooks
https://www.cambridge.org/highereducation/books/an-introduction-to-turbulent-flow/1544AA34040E22C492D357EDCB06810A#overview
https://www.cambridge.org/it/academic/subjects/physics/nonlinear-science-and-fluid-dynamics/turbulent-flows?format=PB&isbn=9780521598866
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