Experimental evidence of accelerated energy transfer in turbulence

We investigate the vorticity dynamics in a turbulent vortex using scattering of acoustic waves. Two ultrasonic beams are adjusted to probe simultaneously two spatial scales in a given volume of the flow, thus allowing a dual channel recording of the dynamics of coherent vorticity structures. Our results show that this allows one to measure the average energy transfer time between different spatial length scales, and that such transfer goes faster at smaller scales.

Figure 1

Top: Partial view of the experimental setup. Bottom: A schematic drawing of the experimental setup (see text).

Figure 2

Top: Diagram showing the relationship between wave vectors, the volume probed by the ultrasonic beams (shaded region), and the size of the disks. The dark circle represents a cut of the vortex core. Bottom: A sample of the anemometer signal. Arrows signal events of minimal air speed, the vortex core being close to the hot-wire probe there. The inset displays the velocity profile of a nonturbulent vortex, which helps in recognizing the vortex core in the turbulent signal.

Figure 3

Top: Power spectral density of the signal displayed in Fig. 2. Three almost linear regions are labeled A, B, and C (see text), with slopes ${\alpha }_{A,B,C}$. The straight line represents the Kolmogorov spectrum, with slope ${\alpha }_K=-1.66$. Bottom: Individual spectra of the signals delivered by the lock-in amplifiers. The spectrum corresponding to the scattering angle ${\theta }_2=60°$ decreases slightly faster with the frequency shift. Scattered waves having the same central frequency of the incident beam have no frequency shift.

Figure 4

Top: Coherence plot of signals detected simultaneously by both receivers, using $q_1=q_2=3.79{\mathrm{cm}}^{-1}$. The wide peak centered at zero frequency shift is due to the vortex. Bottom: Three coherence surfaces are shown, obtained by detuning one of the emitters by a frequency corresponding to a shift $\Delta q$ in the wave number.

Figure 5

Time lags corresponding to the coherence surfaces of Fig. 4a, 4b, and 4c correspond to $q_1=3.79$, 7.58, and $11.4{\mathrm{cm}}^{-1}$, respectively. The straight lines are linear fits to the measured points, with correlation coefficient $R^2=0.60$ (0.75, 0.66). Note that the slopes decrease with increasing $q_1$.