The Reynolds number makes flow behaviors scale-invariant across wildly different sizes

Evidence

Reynolds realized that a dimensionless number concocted from all the important parameters must play a role in deciding which situations are similar and which are very different. By similar, we mean, for example, that two objects producing a vortex street are similar, even though one is an island 15 miles across with air flowing around it and the other is a 1 mm fishing line with water flowing around it. Everything else, such as the size of the object, the velocity of the fluid, the density of the fluid, and the viscosity of the fluid, may all be different, but the Reynolds number will be in a certain range known to produce vortex streets. — Eric J. Heller, Why You Hear What You Hear- An…, 1300

Categorization

• DEFINE: Explains what a dimensionless number is and why the Reynolds number unifies scales from a 15-mile island to a 1mm fishing line.
• XREF: Links to my broader why-do-we-hear-what-we-hear question: scaling laws explain how identical acoustic mechanisms recur across vastly different physical scales.
• SEED: The island/1mm fishing-line example is a ready-made illustration for an article on how scaling laws make nature’s physics portable across dimensions.