We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular, the second-order correlation function is diagonal in the shell index and the third-order correlation exists only between three consecutive shells. Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our choice of nonlinear coupling. We demonstrate that the model exhibits multiscaling similar to the GOY model. The scaling exponents are shown to be independent of the viscous mechanism as is expected for Navier-Stokes turbulence and other shell models. These properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevE.58.1811