It's simulated with Adobe After Effects; I would think it's probably broadly accurate, and uses some form of the underlying physics (Navier-Stokes equation) to produce the simulation. In that sense it's reproducing the processes which generate these patterns, as opposed to purely faking it by e.g. playing around with Fourier series to get things which look like waves.

But there's no way it gets the detailed physics right (kinetic energy spectrum, detailed free-surface position) - that's a research-grade problem requiring massive amounts of computer time.