Why do speed boats leave narrow channels in their wakes? I've noticed that when a speed boat goes over very flat water that a channel is left behind that doesn't spread. I've seen this on rivers. I would have thought that the small waves and ripples would quickly return and erase the channel.
In the image below you can see the spreading waves from the wake as well as a channel that neither spreads nor quickly disappears.

What allows this channel to remain for such a long time?
 A: Yeah, by the looks of it there is behind the boat a trough that as you say doesn't widen and that lasts surprisingly long
Here is what I think would need to happen in order to result in a trough like that. You need two vortices of water, side by side, barrel rolling in the wake of the boat. That barrel rolling water then drags surface water outward, leaving that trough.
I'm not sure what process must be forming those vortices. If I hazard a guess, probably the formation of the vortices ooccurs mainly at the front of the boat, where the hull is parting the water.
Later edit:
It just occurred to me: if the boat's propulsion is two counterrotating screws then that could also explain two side by side barrel rolling vortices. The image is too small to see what size the boat is, so I can't see whether the boat in the picture is big enough so that it might well have two screws.
A: Energy is being transferred from the boat to the water by 1) the dynamic action of the boat hull rapidly pushing the water aside and then letting it slosh back and 2) viscosity drag and turbulence which tends to violently stir up the water surface over and through which the boat is traveling, and mix it with air. 
Mechanism 1) sets gravity waves into motion which travel sideways at an angle away from the boat and mechanism 2) churns up and swirls the water around randomly in a shallow zone next to the surface which spreads relatively little. 
That swirling zone full of popping bubbles and small eddies persists long after the gravity waves have departed, which leaves the wake you can see in the photos.
