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Response maxima in modulated turbulence Part II: Numerical simulations

Numerical simulations of fully developed turbulence driven by a modulated energy input rate or driving force are performed within two dynamical cascade models, the GOY shell model and a reduced wave vector set approximation of the Navier-Stokes equation (REWA). The frequency behavior of the system response is studied and compared with predictions from a variable range mean-field theory, which excludes turbulent fluctuations. In agreement with the mean-field approach we find a constant response amplitude for low driving frequencies and a 1/w-decay of the amplitude for high frequencies. In the mean-field theory, the finite cascade time scale had lead to an oscillating behavior of the response amplitude as a function of the driving frequency. In the simulations of both models we observe the main maximum. The higher maxima and minima are completely washed out by fluctuations.