In the following sentence, whose velocity is u—the particles or the medium?
For particles moving in a medium with macroscopic velocity u: The normalized Maxwell’s distribution function (Eq. 1.38) can be written as ..."
In the following sentence, whose velocity is u—the particles or the medium?
For particles moving in a medium with macroscopic velocity u: The normalized Maxwell’s distribution function (Eq. 1.38) can be written as ..."
The key is the word macroscopic. In fluid dynamics the macroscopic velocity is a vector giving the magnitude and direction of the fluid. Individual particles within compressible fluids may have velocities that differ from the macroscopic velocity.
The sentence is, on its face, ambiguous. However, it seems far more likely to me that the prepositional phrase, "with macroscopic velocity u," is modifying the participle "moving", and not the noun "medium". Presumably, it is the motion of the particles that is interesting in this situation. If it were the medium moving with velocity u, then we would seem to be lacking information about the motion of the particles within it.
Unless the context suggests that we're considering particles moving within a medium that is also moving, there seems to be little support for the idea that the medium has velocity u.