You described something like the Eco Wheel turf scrubber. It's currently the only turf scrubber you can buy in the world, and it's $3,000.
Yes the screen can be any shape, including a cylinder, but there are problems...
If you made the screen into a wide cylinder, and rotated it: you'd get perfectly even light coverage - especially if using a tube across the width of the roll.
Problem is the low amount of light; only a small portion of the cylinder is lit up at any given second... the rest are dark.
with a waterfall cascading over one part of the cylinder, you'd get consistent water coverage
Yes, but even-coverage of water is a lesser-important criteria, behind light. So you are hurting your most important critera more than you are helping the lesser.
from what you've said, it sounds like the constant movement would help increase turf growth
It does very much, but a "dry time" (like 60 seconds), similar to how waves work, seems to be just as important. Now, our little waterfall versions can operate without turbulence or dry time. However, dry time can easily be added with a timer; turbulence requires large mechanical setups, like your wheel design, or a dumping bucket design. They are very hard to build... much more so than a waterfall (which is the exact reason I created a waterfall... I did not want to buy that huge Eco Wheel, or a big dumping bucket, which aren't available anymore anyways.)
if it rotated slowly enough, you'd get the pulsing wet/dry cycle without any special pumping, and therefore without periodic loss of function
If rotated that slow (say, 60 seconds), then you lose all your turbulence, which is the biggest advantage to the wheel design.
it would be more compact, so in some circumstances you could fit more screen in to limited space.
I don't think it would be. You actually need more square inches that you would with a waterfall screen, because the lighting is so much weaker. Look at the size of the Eco Wheel and you will see... it's as big as a 100g tank.
Other issues:
How to take the giant wheel to the sink to clean it.
How to get a razor blade into the different parts of the screen.
How to keep the wheel from getting stuck.
Those points aside, I did at one point consider a cylindrical waterfall design using a 5 gal bucket, whereby the "screen" was just the inside wall of the bucket, maybe with actual screen material attached to it. A light could be hung in the middle, and a circular waterfall tube could be placed around the top. It would give about 460 square inches of "screen", which (because it's only one sided) would be large enough for a 230g tank. Problems would be cleaning/scraping (see my cleaning video for the pressure needed to scrape real turf), and just getting the bucket into your sink. But worth some thought. And good thinking on your part
