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It isn't often that the perfect analogy falls into place, but in the case of wave pools, we have one. Essentially, wave pools work on the same principles as another feat of hydraulic engineering and fluid dynamics, the modern flush toilet. Your favorite water theme park might not care for that analogy, but it's surprisingly appropriate and illustrative.
Much like modern flush toilets, wave pools consist of two separate compartments. There is a holding tank filled with clean water supplied by outside lines, and a separate tank filled with...let's just say swimmers. A stopper plugs the drain hole at the bottom of the holding tank, at least until a hydraulic piston forces the stopper out and the water drains out with considerable force.
The secret behind wave pools lies in what happens next. The water is directed downwards at first, then into a channel with a backwards-curling lip. This causes the water to crash into the retaining wall between the two tanks. The impact of this crash, combined with the rising water level, causes a wave to form. It's this wave that moves through the pool area, finally crashing against the shallow end.
Wave pools are remarkably efficient. Some of the water from each wave cycle remains in the pool, while the rest is recovered in side channels leading back to the holding tank. While one wave cycle is occurring, the supply lines refill the holding tank. The number of waves possible during an average day depends on how quickly the holding tank can recover. Some wave pools can recover within a few minutes.
There are some differences between wave pools and other water park attractions. The water in wave pools is not usually as chlorinated as that in a standard pool, since the water is recycled more often. The gradual feathering out of wave pools is no accident, either. Without the choking effect created as the water approaches land, the waves could crash violently on unsuspecting guests. The energy of the wave must be dissipated.
I just wanted to add that blue wave pools are also found on cruise ships. I recently went on a cruise on the Oasis of the Seas, a Royal Caribbean Cruise ship that offered a pool wave machine as one of its amenities.
You had to be at least 52” tall in order to go in. They offered boogie boarding and stand up surfing. Private classes were offered for both types of surfing.
At the end of the cruise they even had a surfing contest. It was a lot of fun to watch.