So: Is the close similarity of small waves crossing water of varying depths ("depth potentials") an example of an approximate gauge invariance?
If so, do other "only the surface dynamics matter" visualizations exist for more complicated gauge theories, ones that might help students understand them better?
Finally and more speculatively, would the depth-dependent forms of large waves (think surfing) have any useful tutorial parallels to broken symmetries?
(This question is mostly a sanity check. I like good tutorial visualizations, but only if they remain true to the original physics.)