Viscous Effects on Inertial Range Scalings in a Dynamical Model of Turbulence

A class of Gledzer-Ohkitani-Yamada shell models for fully developed turbulence is studied numerically in the presence of a hyperviscous damping $\nu k_n^{2+\alpha }$. It is found that the inertial-range scalings ${\zeta }_p$ ( $〈|u_n{|}^p〉\sim k_n^{-{\zeta }_p}$) are not universal, but depend on the hyperviscosity index $\alpha$. A class of anomalous scalings are observed, and remarkably ${\zeta }_p/{\zeta }_3$ are universal. A theoretical explanation is developed based on a recently proposed scaling model of turbulence [She and Leveque, Phys. Rev. Lett. 72, 336 (1994)].