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If we did a thought experiment and imagined the Earth to be covered in a global ocean (ie. no land to slow winds or direct ocean currents) would winds and waves be perpetually enormous or would they come to some sort of equilibrium state?

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They would come to equilibrium, or rather steady state, at which energy input ultimately from the Sun matches energy dissipation by friction. The wind speeds would be somewhat higher because water presents less friction than land, but not higher by a huge factor. This state of affairs exists to a good approximation in the prevailing westerlies of the Southern Hemisphere --- the Roaring 40s.

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A few thoughts - assuming like you say that the aqua-planet is the same size as earth, and all else being equal, it's best to consider the two major classes of waves:

Nondispersive wind generated waves: Here the maximum wave height is a function of wind speed (fetch). However, wind speed in general is not a function of wave height (unless you invoke concepts like walker-circulation from ENSO, but you wouldn't get ENSO since there are no continental boundaries).

The relationship between maximum wave height and fetch in deep water, can be described empirically as $$H_{max}=0.332 \sqrt{F}$$

So this all goes to say that it is impossible to determine $H_{max}$ without knowing something about the atmosphere dynamics. If you assume that the atmospheric dynamics are the same as on earth (in terms of storm statistics), then this little empirical relation would suggest wind generated wave heights should be no different for an equally sized aqua-planet. Larger planets do however have larger storms...

Eddies and planetary waves Eddies are waves, yet quite different from wind generated waves. While they certainly don't reach the impressive heights of wind-generated waves, their wavelengths are several orders of magnitude larger. And so technically, you could say they are in fact "bigger" waves. Along with eddies, there planetary waves such as Rossby waves and Kelvin waves. All these eddies and planetary waves are limited in size by the Rossby radius of deformation. Which is to say, their maximum size is effectively limited by the curvature of the earth.

Upshot To get larger wind generated waves, you need larger storms. Therefore you need a larger planet (e.g. great red spot on jupiter). To get larger planetary waves and eddies, you also need a larger planet! The reason that larger planets have both larger storms and larger planetary wave/eddies is the same ~ which is that the rossby radius is bigger for a bigger planet.

You might be interested to check out something called the "aqua planet experiment" project. These are general circulation models run on a hypothetical planet with no continent, they're all just atmosphere and ocean. The image below is cloud cover output from an aqua-planet simulation. aqua planet

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