The Ha peak intensity, velocity shift and velocity dispersion maps of the giant HII region NGC 604 in M 33, obtained by two dimensional high spatial resolution Fabry-Perot observations with TAURUS II at the 4.2 m William Herschel Telescope in Spain (Sabalisck, 1995), 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 $\sim$ 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 as either 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 $\sim$ 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 $\sim$ 70 pc where a low wave number turn over is observed; if true, 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, $\sim$ 70 pc. In both cases the average intrinsic optical depth consistent with the results is $\sim$ 20 pc.

27 pages, postscript version including 8 embedded figures