Wow, welcome to all the new contributors!!
In terms of wave vs not a wave -
A transverse wave is motion of energy where the particles don't actually move in the direction of energy. It's why you can be floating in the ocean and have a wave come at you at 20mph, it lifts you up 6ft in the air and then brings you down before it continues on its way. The wave has moved forward but you, and the water you're in haven't...
A standing transverse wave is where the wave bounces back or two waves collide in a controlled space so they no longer exhibit a propagating wave. So, instead of the wave pushing you up and down while it moves forward, the waves cancel and now: you move up and down and there is nothing moving forward or backwards.
A longitudinal wave (like a sound wave) is one where the up/down wave action happens to be forward/backward instead. The particles still don't go anywhere in the end, only the wave actually goes. Locally, the particles move forward and backward due to the pressure that they feel as the wave passes them.
A standing longitudinal wave just has particles moving forward and backward without a propagating wave. If you've ever watched people making styrofoam balls dancing with sound.. That's what it is. In concept, this looks like what I want... The problem is that water is hard to compress and acoustic waves in water move very very fast. I went down this path for a few days - it may still be viable but out of scope for now.
All these waves are just the beginning for a real water wave. In water that has an exposed top, a wave is neither transverse or longitudinal only. Basically, the parts of water pushing air are moving differently that water pushing water... This actually causes water to not just move up and down, or forward/backward. It makes the particles go in vertical circles of different sizes as you go up and down the wave's height... This results in a trochoidal wave...
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/watwav2.html
So is an alternating flow the same as a wave? Take the gyre that Mike is working on. Different time scale but it's a circular flow that alternates. There's a wave that gets it started, but once it's running, the flow is just a loop. No up/down. No front/back. So I'd say it's not a wave until he reversed the flow. At that point, the wave is the result of acceleration/deceleration. The reverse flow in the end is also not a wave after it settles.
Keep the idea that a wave moves a lot forward but the particles only go up/down. A standing wave has no motion forward, you only have the particles going up/down.
So an alternating gyre (looping flow) is closest to what I'm trying to do.
Open vs. closed top... Because water is mostly incompressible, if it has no air to push out into, if you push it with a piston or pump in a closed loop sealed pipe, it will all go... Bulk flow. It you open it to air by drilling a hole, it will push out into the air instead. With an open tank, the water pushes up and makes a surface wave. This is why I seal the ducting n the back and use baffles to direct the flow forward with submerged outlets and inlets.
Another significance of the gyre concept is where the water goes when you pump it in. With my surge now, the water level rises by 1.5" before my weir end to end overflow brings it under control. In a gyre, the should be no net upward wave. The water being pumped in is also being pulled out.
So bulk flow isn't a wave. Making an alternating bulk flow that alternates without creating waves... That's the tricky part.