I'll try to explain as best I can based on some fluid dynamics education from long ago.
I'd design the "end" of the river to be at about a 3-4 foot depth and the "start" of the river to be at an 8-9 foot depth. The intake of the pump being in the "end" and the output being in the "start".
Depending on your shape and topography, you can use the intake and output in a synergistic way. Using a smooth bore 12 inch PVC pipe with the inlet in the shallow end of the river and the air diffuser pipe TEE in the deepest part, allow the air to have the longest length of rise possible before the bubbles reach a long radius 90 degree elbow pointed in the direction of flow wanted...I would imagine a minimum of 3 pumps would be needed to gain a slow circular flow, and it may require 100 or more feet of pipe in total depending on intake and outflow locations. Put gradual shallowing section of the river in a fairly straight length of river, and then a sharp curve and depth drop into the deep section.....I hope you can visualize my thinking here, as I am terrible at drawing