FURTHER RESULTS ON MULTIFRACTALITY IN SHELL MODELS

Very long integrations, involving hundreds of millions of time steps, have been performed for the Gledzer-Ohkitana-Yamada ''shell model'' of fully developed turbulence, thereby allowing the computation of essen tially noise-free structure functions at all inertial- and dissipation -range scales. Previously reported results by Jensen et al. [Phys. Rev . A 43, 798 (1991)] on the multifractal behavior of this model are con firmed. Oscillations in the structure functions are found to be genuin e. An exact relation for certain cubic moments, equivalent to Kolmogor ov's four-fifth law, is derived and tested. The third-order structure function, here defined in terms of the third moment of shell amplitude s, is not directly determined by this relation and need not have its e xponent equal to one. Significant discrepancies are actually found whe n the ratio between successive shell wave numbers is less than two.