One way to deal with a dead spot is with an air lift. Now, I don't know what you know, so forgive me if I over-explain.
An air lift is nothing more than a pipe that is vertical in the pond, one end just above the bottom, the top anywhere from just below the surface, to just above the surface, with an air stone somewhere in the pipe, near the bottom. The rising bubbles from the air stone pushes water up the pipe, drawing it in from the bottom, and lifts it out the top.
If that pipe has an elbow on the top, the water will flow out of the pipe and can be directed in any direction. Doing this will create a flow where there was none before, and help "turn over" the water by bringing water (and some sediment usually,) from the bottom of the pond to the top.
Using the elbow will make a bit of a noise, so you can use a "Y" fitting instead. Cut the pipe back so one part of the "Y" sticks up above the water, and the horizontal part of the "Y" is about half-submerged. The bubbles will come straight up and out thru the top of the "Y" fairly quietly, while the water will flow out of then horizontal part of the "Y." And you can simply drop the air stone right down the top of the "Y.'
I ran a 25 watt UV in a small pond using an air lift much as described with only a small aquairum pump to power the water thru the light tube. Worked great, used less power than a pump would have, and it also added a bit of oxygen to the water. If this description is kind of hard to follow, I will try to find a picture of it and post it. But is really is quite simple to set up and run.
Mike S.
Spring Hill, FL