temperature of flowing fluid

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote:
>  There is such a thing as a
> Maxwell-Boltzmann distribution, which differs from the
> plain old Boltzmann distribution by a uniform shift in velocity.

Robert B Zannelli was suspicious of this.

I spent a few minutes looking and found precisely no
references that back up my assertion.  Perhaps this
is just a memorrhoid of mine.

But ever since I was a sorcerer's apprentice, I've
been writing the Maxwell-Boltzmann distribution in
the form
        exp(...(v-v0)^2)
where v0 is the velocity (in my frame) of the overall
flow of the fluid.

You might object that in equilibrium, the fluid isn't
flowing at all, but I would retort:
 a) That can't be true in general;  if my frame is
moving relative to your frame, the fluid can't possibly
be at rest in both frames.  Temperature is defined in
(and only in) the frame comoving with the fluid, but the
velocity of the individual particles is well-defined
in all frames, and surely must be given by the formula
mentioned above.
 b) There may be some reason (e.g. a conservation law)
why the fluid will come into equilibrium with itself
on a timescale much shorter than the timescale (if any)
on which it will lose its overall velocity.

Remember, equilibrium is when all the fast things have
happened but the slow things have not.

If anybody knows the official name of this velocity-shifted
distribution, please let me know.  In the meantime, I will
continue to call it the Maxwell-Boltzmann distribution, and
consider the v0=0 case to be just a special case thereof.