Acceleration Correlations and Pressure Structure Functions in High-Reynolds Number Turbulence

Abstract

We present measurements of fluid particle accelerations in turbulent water flows between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, non-intrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our experimental data provide strong support to the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high Reynolds number turbulence by Obukhov and Yaglom in 1951. The measured pressure structure functions display K41 scaling in the inertial range.

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

“…Mordant et al (2004a) set up another high-Re λ experiment and measured Lagrangian trajectories using high-energy physics particle detectors, which allowed them to retrieve only short-time statistics: the extreme temporal resolution of their system allowed them to fully resolve the highly intermittent Lagrangian acceleration signal at Re λ ≃ 700 (roughly 70 data-points per τ η ), and to quantify its decorrelation time. The same experiment was repeated and the flow was measured with a more standard high-speed camera system (Xu et al, 2007), confirming the same findings. The experimental and numerical studies of Guala et al (2007) and Biferale et al (2008) quantified the bias due to a finite measurement volume, typical of laboratory experiments.…”

Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

“…This leads to the long-time correlation of the acceleration norm, versus the short time correlation of its orientation (of the order of the Kolmogorov time). Previously, this was observed in high-Reynolds-number HIT: see experiments by Voth, Satyanarayan & Bodenschatz (1998), Voth et al (2002), Sawford et al (2003), Mordant, Crawford & Bodenschatz (2004b) and Xu et al (2007), numerical simulations by Pope (1990), Vedula & Yeung (1999), Tsinober, Vedula & Yeung (2001), Sawford et al (2003) and Yeung et al (2006) as well as development of models by Monin & Yaglom (1981), Pinsky, Khain & Tsinober (2000), Hill (2002), Sawford et al (2003) and Lamorgese et al (2007); see also the review of Toschi & Bodenschatz (2009). Consequently, for HIT there is an underlying suggestion of time-scale separation of the norm and orientation of acceleration (Pope 1990;Mordant et al 2002Mordant et al , 2004aSabel'nikov et al 2011):…”

Where do small, weakly inertial particles go in a turbulent flow?

“…A spherically shaped measurement volume with a diameter of 22 mm was located at the centre of the water chamber, where the mean flow was small compared with the velocity fluctuations. The spatial resolution of 45 µm per pixel and the temporal resolution of 31 frames per Kolmogorov time τ η guaranteed accurate measurements of particle velocity and acceleration (Xu et al 2007). As shown in the table 1 we used three different types of particles: polystyrene, glass and stainless steel with densities between 1 ρ p /ρ f 8.…”