Thinking about curl in the cafe at Maryport Aquarium

The log burner in the cafe at Maryport Aquarium had a fan on top. I've never seen a device like it. I had hoped it was being driven by the hot air rising from the stove but there was a wire on the back...
Unplugged, such a paddle wheel would be a means of determining whether or not a vector field has curl. Without a battery, this wheel will only turn if the upwards flow of air on one side is stronger than the upwards flow of air on the other. If that is true, then the vector field for air flow above the stove will have the property called curl.