Turbulence modification by periodically modulated scale-dependent forcing

The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier–Stokes equations. The forcing is modulated via periodic energy-input variations at a frequency x. Harmonically modulated forcing of the large scales is shown to yield a response maximum at frequencies in the range of the inverse of the large-eddy turnover time, as well as a characteristic rapid change of the phase-angle between forcing and response. Harmonically modulated broadband forcing is also studied in case a wide spectrum of length-scales is forced simultaneously. If smaller length-scales are also explicitly agitated by the forcing, the response maximum is found to occur at higher frequencies and to become less pronounced. In case the explicitly forced spectrum is sufficiently wide, a response maximum was not observed. At high modulation frequencies the amplitude of the kinetic energy response decreases as 1/x, consistent with theoretical predictions. The amplitude response to intense pulses of energy injected via a square-wave modulated forcing at the largest scales was also studied. This forcing protocol induces a more complicated response structure that also displays a maximum in the kinetic energy amplitude response at a modulation frequency comparable to the harmonically modulated case