Is the definition of streamline by NASA correct?

Question

This question defines a streamline as NASA do, i.e. by looking at air particles movement. But I'm confused by special cases:

• if there is no wind, air particles are still moving, but we take the average movement on all point we get a field of null velocities.
• given this answer, it seems that NASA call "air particles" a fluid particles and not real particle, but I'm not quite sure.

In short, is the NASA definition making confusion between "streamline" and "line of flow", "air particles" and "small volume of air containing several air particle whose average movement follow a streamline"? Are the terms used by NASA the correct one?

EDIT: I asked NASA and they respond with a redirection to a definition that speaks of flow and "massless particle" without defining either one. Yet speaking of "massless particles" clearly states they are not actual air particles. I still feel as if I'm in front of circular definitions, concept A defined by concept B, and concept B defined by concept A, if ever defined.

Answer 1

It is essential to understand that English is a flexible and somewhat fluid language in which, as Humpty Dumpty one said, "When I say a word, it means exactly what I want it to mean". What you and NASA mean by a "particle" is not the same.

In classical Newtonian mechanics a particle is a macroscopic concept; we all know that a particle is a very small lump of solid matter. But at the quantum scale of individual molecules the concept begins to fuzz out into general weirdness, governed by the Schroedinger wave equation and Heisenberg uncertainty principle. Nevertheless quantum physicists talk of "particles" with gay abandon, in full knowledge that these things are just probability waves until someone looks for them. So a "particle" means different things to different physicists.

Mathematical treatments of fluid mechanics have a different concept of a particle again, derived in large part from the calculus or "mechanics of infinitesimals". To such a mathematical physicist, a particle is a volume large enough to ignore things like thermal motion of molecules, but arbitrarily small on the macroscopic scale of Newtonian mechanics, such that its spatial dimensions are negligible - infinitesimal, even.

Given such a "particle", its line of flow is indeed a streamline. One might pedantically define a streamline as the mean path of certain air molecules, but then one has to define which air molecules and one is forced back to the particle definition in all but name.

So within the context of mathematical analyses of air flowing over an airfoil, NASA are perfectly correct.

Answer 2

The velocities of individual particles (molecules) in a gas are described by the Maxwell–Boltzmann distribution. This is random thermal motion and is unrelated to streamlines. To describe streamlines we must think of small volumes containing many individual particles. These small volumes can be regarded as idealised particles following streamlines, although they are not true particles. They contain many molecules, and individual molecules enter and leave them. I would not say there is a rigorous correct definition of "air particle" but it should be clear from context whether we are talking of true particles or small volumes.