The Ha peak intensity, velocity shift, and velocity dispersion maps of the giant H II region NGC 604 in M33, obtained by two-dimensional high spatial resolution Fabry-Perot observations at the 4.2 m William Herschel Telescope in Spain, are analyzed via two-point correlation functions. The whole system seems to rotate as a rigid body on scales from 50 to 80 pc (the largest studied scale), with a period of approximate to 85 Myr. We demonstrate that the cloud seems to be comprised of eddies with varying characteristic scale lengths which range from 10 pc to the largest observed scales. The calculated kinetic energy spectrum may be interpreted either as a manifestation of a double cascading spectrum of forced two-dimensional turbulence or as a Kolmogorov three-dimensional turbulence (although this last possibility seems unlikely). According to the first interpretation, turbulence is being forced at scales of approximate to 10 pc, while an enstrophy (mean square vorticity) cascade has developed down to the smallest scales resolved and an inverse kinetic energy cascade extends up to scales of approximate to 70 pc, where a low wavenumber turnover is observed; if this interpretation is correct, this would be the first time that such a phenomenon has been observed outside the solar system. As for the second interpretation, energy should be injected at the largest scales, approximate to 70 pc. In both cases the average intrinsic optical depth consistent with the results is approximate to 20 pc.