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We investigate the regime of fully developed homogeneous and isotropicturbulence of the Navier-Stokes (NS) equation in the presence of a stochasticforcing, using the nonperturbative (functional) renormalization group (NPRG).Within a simple approximation based on symmetries, we obtain the fixed pointsolution of the NPRG flow equations that corresponds to fully developedturbulence both in $d=2$ and $d=3$ dimensions. Deviations to the dimensionalscalings (Kolmogorov in $d=3$ or Kraichnan-Batchelor in $d=2$) are found forthe two-point functions. To further analyze these deviations, we derive exactflow equations in the large wave-number limit, and show that the fixed pointdoes not entail the usual scale invariance, thereby identifying the mechanismfor the emergence of intermittency within the NPRG framework. The purpose ofthis work is to provide a detailed basis for NPRG studies of NS turbulence, thedetermination of the ensuing intermittency exponents is left for future work.

Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution