It will probably use profile wire with dozens of turns. But that depends on the voltage. 2 MW at 400V will be in the kA, a bit much, so it will probably be 6 or 10 kV.
[Here](https://www.youtube.com/watch?v=5P6YVi2mB6Q) is a video of someone repairing a standard 400V generator. Each bundle is one coil, which will be put in series depending on the voltage configuration.
We rewind low voltage generators at work, I might be able to ask there tomorrow.
*Video is not my work, but some competitor.*
*Edit: I checked, we haven't repaired a wind turbine generator for years. We only certificate (test) and store them.*
This is actually a very difficult question to answer.
A 2MW wind turbine in the US (60Hz) will _probably_ have a 690V 3-phase 6-pole doubly-fed induction generator with a synchronous speed of 1200 RPM (note: the generator assembly, including electronics, is _not_ synchronous overall, but the machine itself has a synchronous speed of 1200 RPM; see Edit 2, below).
This means that it will have at least 3 armature windings (one per phase) and 3 field windings (one per pole pair). So there are at least 6 copper coils, not just 1.
Part of the reason why it's hard to say how many turns there are is because, even within the assumptions above, there are a plethora of different generator designs that will, more-or-less, achieve the same result. For example, the number of slots in the armature could change the number of turns by a factor of 2. Put more turns on the field windings, or more current through it, and you need fewer armature windings. Change the way the windings are wound (lap winding, wave winding, ...) and the number changes again.
The upshot is that nobody in the wind industry or academia thinks of "number of turns" as being an important characteristic of the generator. This is the domain of a handful of generator design specialists in companies like GE and Siemens who actually make the generators themselves. So, I think you're unlikely to get a good answer to this question.
In general, the output voltage from the armature windings is a function of the magnetic flux (due to the field windings) and the number of turns. The magnetic flux, in turn, is a function of the field current and number of turns. As a rule, you would expect "many" field windings and relatively few armature windings for a low-voltage machine such as this.
If I had to make a semi-informed guess, I would think that the most likely number of turns on each of the 3 armature windings would be "dozens" (based on a one or two layers of a handful of turns in each of 12 or 24 armature slots), while the most likely number of turns for the field windings would be "hundreds" (300? 800? I have no idea).
Edit: in the US (60Hz), the generator is probably 6-pole, rather than 4 (as originally posted). 4-pole generators in wind-turbines are more common in 50Hz countries, e.g. the venerable Vestas V-90 1.8/2.0 MW turbine uses a 4-pole generator for 50Hz and a 6-pole for 60Hz.
Edit 2: There was a bit of confusion here (comments below). AC machines are just arrangements of iron and copper. The mechanical rotation of the shaft bears a fixed relationship to the frequency of the AC output (for a generator) or input (for a motor). In wind turbine DFIGs, clever electronics provide the illusion of asynchronous operation, but the machines themselves are unchanged and have "a synchronous frequency" despite being used in asynchronous service.
From experience on Enercon wind turbines, they run a direct drive synchronous generator. This generator, when operating at full output, is typically only turning about 17 rpm, and produces 400 volts, 3 phase power. The generator is wound manually in the factory and I believe each coil is 58 turns, and then 2 parallel coils per slot, (4 coils essentially), for the 2 MW machine.
Ok, what is happening in this thread? Why don't wind turbine enthusiasts understand how to answer a question?
Instead, it's endless "oh, it depends on such and such variables" - duh! Everything does. We're asking what the TYPICAL NUMBER OF TURNS is.
If someone asked, "how many transistors are there in a typical 2017 cpu" (it's about 1 billion), the people in this thread would endlessly say "it's impossible to determine" rather than actually using their knowledge to help inform.
I think offering a calculated approximation can be done using the link provided...19rpm at 660V nominal output, and perhaps a built in transformer.