Critical "dimension" in shell model turbulence.

We investigate the Gledzer-Ohkitani-Yamada (GOY) shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an "effective dimension" between d=2 and d=3. We identify a critical point between these two situations where the flux of energy changes sign and the helicity flux diverges. Close to the critical point the energy spectrum exhibits a turbulent scaling regime followed by a plateau of thermal equilibrium. The corrections due to intermittency persist close to the critical point. We identify scaling laws and perform a rescaling argument to derive a relation between the critical exponents. We further discuss the distribution function of the energy flux.