my waves professor is so funny
someone asked him why the models we use only work for small amplitudes and he said
"well, i'll demonstrate!"
then he started slowy sliding a tub of water back and forth harder and harder until it spilled all over the desk and on his clothes
"uh oh!!!!
... does that answer your question"
@imyxh Eh, that's somewhat misleading. There are things that break way earlier than at such a discontinuous transition: things become nonlinear (e.g. the pendulum's period being independent of amplitude is only true in small amplitudes).
@timorl Well, but that's a consequence of the discontinuity. I wanted to say that things break down way earlier than that (for waves in a container, when they're a nontrivial fraction of the water depth the things are way past breaking down). @imyxh