I hope that I'm able to explain this!
The foam is a thin cloud layer. It's masked with another cloud fractal that's
vertically animated through a transform shader to get some kind of turbulence. The same cloud fractal is also used as a breakup shader for a white material to get the foam patterns inside the wake. As I said it's only animated vertically. To make it move with the ship I merged the cloud fractal mask with a painted shader that has the shape of the wake and is animated with the ship. So the cloud fractal stays in place but is made visible where the animated painted shader appears.
For the white caps I used the same masking technique but animated the cloud fractal additionally in the horizontal direction in sync with the wave patterns of the lake object's water material.
Btw here's a lighting test