IMO, choking mass flow clearly reflects the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_c c$ where $\rho_c$ is the critical mass density and c is related to the speed of sound (see Landau-Lifchitz section 83). Should this result also hold in transient flows, IMO, the Navier-Stokes Equations should be modified so that they explicitly exhibit pseudo-Lorentzian symmetry (in momentum density) instead of Galilean symmetry. The momentum density field would then become explicitly causal.
IMO, the velocity field does not make any sense if detached from the mass density field.
Gert Van der Zwan:
This paper seems to be a formulation of relativistic fluid dynamics, which is very useful in plasma physics. However, my question did not address this subject. What I had in mind was the fact that, in a stationary fluid flow, from thermodynamic considerations, it can be proven that:
d(\rho v)/dv=\rho[1-v^2/c^2]
Landau and Lifhchitz, "Fluid Mechanics", section 83.
where $\rho$ is the mass density, $v$ the local velocity and $c$ the local speed of sound. This indicates that the momentum density does have a maximum, at least in stationary flows (where the local velocity is equal to the local speed of sound).
Since the momentum Navier-Stokes equations are Galilean invariant, a sufficiently large pressure gradient should make possible to attain larger momentum densities and this contradicts the previous equation. I was wondering if one should not enforce the maximum local momentum density as a pseudo-Lorentzian symmetry. (In incompressible flows, at least, I think that one does need to enforce this symmetry).
Kind Regards,
Carlos Janer.
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