  Recent numerical results show that if a scalar is mixed by periodically
forced turbulence, the average mixing rate is directly affected for forcing
frequencies small compared to the integral turbulence frequency. We elucidate
this by an analytical study using simple turbulence models for spectral
transfer. Adding a large amplitude modulation to the forcing of the velocity
field enhances the energy transfer and simultaneously diminishes the scalar
transfer. Adding a modulation to a random stirring protocol will thus
negatively influence the mixing rate. We further derive the asymptotic
behaviour of the response of the passive scalar quantities in the same flow for
low and high forcing frequencies.
