Is there some limit to the height of ocean waves that has been calculated based on fundamental physics? I became aware that when surfers try to surf on record breaking waves they can no longer paddle in, and must be towed in with a jetski. Taller waves move at a faster speed than shorter waves and since you must match speed with the wave to surf it, paddling no longer suffices, and you must get additional propulsion. Taller waves are faster than smaller waves (but waves also slow down when they compress and become taller so that's a little confusing).
Given that's the case it got me thinking about the largest waves that have been recorded, whether ocean born waves driven by wind or generated by megatsunami (distinguishing runup from wave height). In both cases, the maximum height I can seem to find is about 100/30m-200ft/60m for apocryphal waves, and recorded waves (such as the Draupner wave) have been recorded between 80ft/20m-100ft/30m. A reasonable assumption would be that natural processes already put in enough energy to reach the maximum wave height. Considering that even a megatsunami like the Lituya Bay event only produced a 100ft/30m-200ft/60m wave (it is the much higher runup height on land that is usually quoted) I would suspect this, but I don't have any way to prove it. I've seen asteroid strikes quoted as producing much larger waves but I'm skeptical about considering these to be waves more than gigantic splashes.
If a wave was large enough that it was travelling at the speed of sound then it would obviously come apart into droplets and expand like the shockwave of a nuclear weapon, and it would no longer be a conventional wave. Other than that obvious extreme is it possible to use the laws of physics to set a limit on water wave height before it must collapse/fall apart?
 A: Bouncing around the web,
From CDIP

[W]ave height is limited by both depth and wavelength. For a given
water depth and wave period, there is a maximum height limit above
which a wave becomes unstable and breaks. In deep water this upper
limit of wave height - called breaking wave height - is a function of
the wavelength. In shallow water, however, it is a function of both
depth and wavelength. (Studies suggest the limiting wave steepness to
be H/L = 0.141 in deep water and H/d = 0.83 for solitary waves in
shallow water.)

Professor Mitterer, among many, presents a "rule of thumb" that deepwater wave height is limited by the ratio $\frac{Height}{Length} < \frac{1}{7} $ .
For short-term peaks, the so-named "Rogue Wave" phenomenon, where several waves interfere constructively, the wave height can be much greater.
My impression after skimming this training manual is that there's no theoretical limit to height so long as you obey the rules about maximum slope ( thus height to wavelength ratio) .  Cue the usual caveats about an infinitely deep ocean on a flat Earth etc.
