Let me back up. I suspect that when people observed other people "throwing someone down" on the ground, they perceived a downward force. Makes sense in a rudimentary sort of way: if we want uke to go down, we force or push him down, right? Well, the obvious flaw in that line of thinking is that uke has two legs underneath him, which supports him against any downward motion.
The thinking, then, is to extend uke with horizontal, lateral movements, parallel to the ground. This gets his shoulders and hips out of alignment with his feet, so his center of balance is now hanging out in space somewhere (in front of him, behind him, to the side, etc.). Keep moving, and eventually, he'll fall down.
Which is great when it works. Problem is, I've noticed that it doesn't always work. Or rather, it does work (quite well)—but only up to a point. What I mean is, I've watched time and time again as tori begins his horizontal movement, successfully gets uke extended and his center of gravity out past his feet, only to end up walking around the mat with uke stumbling right along with him. Sure, he's in a terrible position, but he isn't falling, either. Of course, he may try to get out of that conundrum and we can send him flying the other way by using his recovery motion against him, and that's solid; I've seen and felt that millions of times.
But why can't the first technique work? Why did we have to rely on #2 or #3 to get the job done?
So lately, I've been thinking about moving more like a wave. I'll start everything with a horizontal motion, but once his alignment is disturbed and his center of gravity is hanging out in space, I noticed something. He is now depending upon me to keep his balance. Our centers are no longer two independent things moving around in space; rather, now he's relying on that point of connection between the two of us to hold himself up!
Which means, I don't have to push down to get him to fall; all I have to do is lower my hand (or lower my center, if necessary, bending at the knees, of course). You just gently set him down.
That natural sinking and rising and sinking again starts to look and feel like a wave.
This whole phenomenon is most pronounced in techniques like ude gaeshi, aiki nage/irimi nage, shiho nage, gyakugamae ate, even waki gatame and kote gaeshi. There's a natural "downward" arc at the end that tends to sit uke down every time. Again, I'm not pushing him down. Never, never, never. In fact, nothing changes at all, and I keep moving. Uke doesn't really know what's happening, only that he's sinking. Uke never perceives a change: I never speed up, crank harder, add more force or anything.
It only works, remember, if I A) break down his posture first, get his center out from over his feet, and B) keep my butt moving.
I'm just letting my hands drift down at the end, after the crest, as we move, gently escorting him to the ground. The feeling is very much like being sucked in by the undercurrent until a literal wave comes crashing down on you.
Maybe this isn't new, maybe I should have figured this out a long time ago, but it sure is fascinating...