Can a submarine be powered by a wind turbine? This is not intended as a realistic way for propulsion of submarines, it is just an interesting thought experiment.
Say I want to travel directly towards the wind, only powered by the wind. This is obviously possible on land, as I can just stop, anchor to the ground for some time, and charge a battery. Then I can use the stored energy to drive for a while.
But is this also possible if it is not possible to anchor to the medium I am travelling through? I assume that I can have a net forward movement as I can gear down from a small amount of quickly moving air to a large amount of slowly moving water, but the actual relationship seems kind of tricky.
Is it possible for a submarine powered by a wind turbine to travel directly against the air-flow?
 A: It is possible in theory but not realistic as you said in your question. You have to pay attention to anchoring mechanism. In water you can partially anchor by spreading a big sheet inside the water. The sheet should be spread in perpendicular direction to wind movement. This way, you can charge a battery while the submarine will move little backward. After the battery is charged, you can change the direction of the sheet in parallel to the submarine movement and get some distance covered by battery (in excess of backward movement while charging). You also will have to bring down your wind turbine under water after charging. It is possible but very inefficient.
Spreading the sheet perpendicular while charging, and then making it parallel to submarine movement while moving forward, is equivalent of tying and un-tying your anchor on land, though not as efficient.
A: Whether it's a submarine, boat, car, whatever, if there is a propeller being driven by the wind it can provide forward motion, even directly upwind.
Here's an example.
If you're a high-speed wind sailor, you know why.
You can sail upwind close-hauled, and the only thing that limits your speed is your drag in the water.
Now suppose you tack back and forth - your progress is directly upwind.
An easy way to tack is to mount your sail on an axle so it can just go around and around.
Then you can go upwind, downwind, any way you like, speed limited only by drag.
A: This is not possible.  The wind turbine has an efficiency that is somewhat less than 100%.  The electricity generated by that wind turbine will power a motor that drives a propeller on the submarine, and the motor and propeller each have an efficiency that is somewhat less than 100%.  By the time all of the efficiency losses are accounted for, conservation of energy requires that the submarine floats continuously backwards as the wind turns the wind turbine.
