An alternative understanding says that the Reynolds number is not intrinsically meaningful in the way you are hoping. This is visible in the fact that it makes reference to the size of the system: what size? Is it a radius or diameter or circumference of some round object? What if that object is not round but square? I have a propeller on the front of the plane, do you want the thickness of the blades or the length of the blades or the full length of the airplane? These vary by several orders of magnitude.
Rather, the Reynolds number is a convention tied to a certain geometry. It comes from trying to normalize the Navier-Stokes equations in the context of that geometry: that geometry defines a characteristic fluid velocity (maybe the speed at infinity), and a characteristic size scale, and a characteristic air density. However you define those things, they give you a characteristic length, time, and mass: we divide every unit-ful number in our problem by these units to find a unit-less version of that number in our geometry, and so cast the Navier-Stokes equations into unit-less form. One of the dimensionless parameters that is left in the equations is the Reynolds number, which becomes a promise: if you wanted to study this system in a different fluid or in miniature, if you get these dimensionless parameters to all be exactly the same, the two systems are governed ultimately by the same equation and must do the same thing. The geometry and the dimensionless parameters determine the behavior, always.
Now of course it doesn't represent nothing just because it does not have one universal declaration: it represents in its relative sense either the reciprocal of the viscosity of the fluid, or equivalently we can take the viscosity as a given and it represents the scale of the fluid flow speeds at infinity. Twice the Reynolds number means “I want to study the same system in a more syrupy fluid” or “...at a higher driving speed” equivalently. But different geometries have different senses of how syrupy or fast a measurement of “1” is.