Interesting. The 200 meter thing has seemed counterintuitive to me but it’s not just mixing due to waves. Currents are set up, turbulence is involved.
Good article here:
http://www.hurricanescience.org/science/science/hurricaneandocean/
Three-dimensional cartoon of the temperature distribution in the upper ocean and the impact of a hurricane passing over the ocean when the oceanic mixed layer is thin like much of the Gulf of Mexico (left) and thick like the Caribbean Sea (right). In both cases, the hurricane propagates down and left over the warm sea surface (red), creating a cold wake behind the storm as colder water (blue) is brought towards the sea surface by the hurricane’s wind stress. If the oceanic mixed layer is initially thin (left), the cold wake is colder so the hurricane remains weaker than if the oceanic mixed layer is initially thick (right), all else being equal. Image credit: National Geographic Magazine.