Response maxima in modulated turbulence

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second-order moment of the large-scale velocity difference $D(L,t)=《\left(\mathit{u}\mathrm{}\right(x+L\left)\mathrm{}-\mathit{u}{\mathrm{}\left(x\right))}^2》\propto {\mathrm{Re}}^2\mathrm{}\right(t),$ is calculated for varying modulation frequencies $\omega$ and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average $\propto 1/\omega .$ In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof.