Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence

Table-top rotating turbulence: an experimental insight through particle tracking

“…The linear-logarithmic plots reveal that the decorrelation is roughly exponential, at least till the coefficients drop under 0.4, in good agreement with the relevant literature (see, e.g., Mordant et al (2001), Mordant et al (2004b), Gervais et al (2007)). The exponential decay of the velocity auto-correlation plays an essential role in some dispersion models, strongly characterising them (see, e.g., Sawford (1991)).…”

“…The vertical component shows a deeper negative loop, which might be the effect of the bottom boundary being the only rigid boundary of our measurement domain. These observations confirm well-known features of the Lagrangian acceleration in homogeneous isotropic turbulence, already described for numerically simulated turbulence (see, e.g., Yeung (1997)) and measured experimentally (see Voth et al (1998), Mordant et al (2004b), Mordant et al (2001), andGulitski et al (2007b)). The values reported in literature show a strong dependence with the Reynolds number, as seen for the velocities: the time separation of the first zero-crossing of the auto-correlations of single acceleration components ranges from 2τ η to 10τ η , for Re λ between 140 and 10 3 .…”

“…As expected, the horizontal anisotropy is strongly reduced in the rotated reference frame. The data also support the conjecture that the decorrelation time of the velocity components depends strongly on the Reynolds number, when compared with the data by Gervais et al (2007) (Re λ = 320, first zero-crossing at 142 τ η ) and Mordant et al (2004b) (Re λ = 810, first zero-crossing at 227 τ η ): the first zero-crossing of our auto-correlation curves is observed between 8 and 14 τ η .…”

“…The values reported in literature show a strong dependence with the Reynolds number, as seen for the velocities: the time separation of the first zero-crossing of the auto-correlations of single acceleration components ranges from 2τ η to 10τ η , for Re λ between 140 and 10 3 . Our measurements of the non-rotating flow confirm the general picture, remarked by Mordant et al (2004b): the dynamics of the Lagrangian acceleration vector involves both the dissipative scale τ η (over which it rapidly changes direction), and the integral time-scale (relevant for the evolution of its magnitude). As the authors observed, this statement violates the assumption behind the K41 theory, according to which the acceleration should be independent of the large-scale flow.…”

“…Correlations of velocity were measured experimentally with an acoustic technique at very high Reynolds number (Re λ ≃ 800) by Mordant et al (2001), Mordant et al (2004b). They described a decay of the correlation coefficients of single velocity components proportional to e −τ /τ 0 , with τ 0 comparable to the energy injection time scale.…”