Linear response of turbulence

We study the response of wind tunnel turbulence to perturbations using an active grid. We compare our findings to Kraichnan's linear response result $R(k,τ_d) = \exp(-k^2 \: τ_d^2 \: u^2)$ which predicts a decay of the response with increasing turbulence intensity $u$, wave number of the perturbation $k$ and delay time $τ_d$ since the perturbation was applied (kraichnan.1964). In our experiments we used two different mechanisms to create a perturbation of a pre--existing and well--developed turbulent flow. In the first case we combine both the turbulence generation and the additional random perturbation in the same active grid. We find that the reponse decays with increasing $τ_d$, but much slower than predicted, while the decay was virtually independent of the turbulence intensity. In the second type of experiments, we perturb an active grid-generated turbulent flow using a loudspeaker--driven synthetic jet. The perturbation is at a single wave number $k$, placed well inside the inertial range. The response was found to decay with increasing time delay $τ_d$, while the decay is faster for larger wave numbers, roughly as predicted by Kraichnan's model. However, also in this case the decay rate is independent of the turbulence intensity.