Okay, I know it sounds cheesy....but it works VERY well: we took an old green garden hose and split it down the middle, then cut it into 2 inch sections. We drilled holes in two spots on the hose sections, then fed heavy-gauge wire thru the holes to create re-enforced straps. We poked the straps thru the screen and attached them to the fence posts and twisted the wire tight on the other side. We used 3 straps for each pole and the results were outstanding. I suppose you could use other items (bike iner tubes, rubber mats, etc.), but hose was what we had handy and it worked great! We regularly experience winds of 30-40mph with 50+ gusts and the windscreen is still there. Since the hose is pretty much the same color, you can't see the straps until you're about 20 feet from them. We also have a yellow top-rail cap for the fence, which works well to keep the top of the windscreen secure.
Best of all: It's probably the cheapest solution and it's extremely effective.