Its seems really clear to me how a guitar string vibrates. I can send a wave down a jump-rope by wiggling it the right way. The two fixed ends of the guitar string reflect this wave back onto the string, forcing it to vibrate at frequencies that involve the whole length of the string or an even division of it (the harmonic series). It makes sense that a guitarist can only find harmonics at the even division points (1/2 the string, 1/3 of the string, 1/4 and so on). This produces a series of ascending pitches that are related by all being natural number multiples of the frequency produced by the whole length of the same string.

You can hear this same overtone series produced by brass instruments as the choice of frequencies (notes) that are playable for each given length of metal tubing (The seven different positions on a trombone, for example). The open, full length, guitar string is analogous to the brass pedal note, the lowest note possible on a brass instrument for a given length of tubing. Changing only the frequency of the lip buzz, not the tube length, other notes are "playable". Their pitches correspond to the harmonics played on guitar by tapping approximately at the 12th, 5th, 4th, 3rd frets (and more). All these same notes are available to brass players but notes in between can't be sounded at all, or very unclearly at best.

I see this correlation, but I have trouble imagining how things work with a vibrating column of air to produce a similar phenomenon. A vibrating string is so visual. What is the best analogy to help visualize how air vibrates in a brass instrument?