Control parameter optimization for turbulence shell model

In this study, the control parameters related to the strength of the backward energy transfer in turbulence shell models were optimized using a genetic algorithm. Control parameters of 0.5 and 1.25 produced helicity and enstrophy scaling, respectively. I examined the optimization from the perspective of energy spectra reproducibility. The optimization objective function was the error between the energy spectrum in the inertial and dissipation ranges (derived from the shell model) and the direct numerical simulation results for isotropic uniform turbulence; furthermore, the control parameter was selected to minimize this error. As a result, the optimal control parameter varied within the range 0.47–0.5, with a Reynolds number of 2600–50,000. Using these optimal control parameters, the energy spectrum and turbulence statistics obtained from the direct simulation could be simulated with sufficient accuracy. Moreover, this paper also discusses the eddy viscosity for the shell model. In particular, in the inertial subrange of the energy spectrum, the eddy viscosity produced by the shell model agrees well with the results of the Lagrangian-renormalized approximation.