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

We present measurements of fluid particle accelerations in turbulent water flow 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, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display $K41$ scaling in the inertial range.

Figure 1

Measured standardized acceleration $a^{+}\equiv a/⟨a^2{⟩}^{1/2}$. The symbols are data from the LPT experiment at $R_{\lambda }=460$: $\times$ and $+$ are the two measurements of the radial component, and ○ are the axial component of acceleration. The solid lines are the previous measurement of the radial component of acceleration using silicon-strip detectors in the same apparatus at $R_{\lambda }=690$ [28]. The inset shows $a^{+4}P(a^{+})$, the PDF of $a^{+}$ weighted by $a^{+4}$.

Figure 2

Comparison of the measured acceleration correlation functions with the Obukhov-Yaglom prediction [15] for (a) small separations and (b) large separations. The dashed and solid lines are the predicted longitudinal and transverse correlation functions, respectively. The symbols correspond to measurements from LPT data at different Reynolds numbers. Filled symbols are $R_{LL}$ and open symbols are $R_{NN}$. ▵—$R_{\lambda }=200$, ▿—$R_{\lambda }=350$, ○—$R_{\lambda }=460$, and □—$R_{\lambda }=690$.

Figure 3

Comparison of the measured pressure structure functions with the Obukhov-Yaglom prediction [15]. The solid line is the prediction, and the dashed and dash-dotted lines indicate the $r^{4/3}$ and $r^{2/3}$ power laws, respectively. The symbols are measurements from LPT data at different $R_{\lambda }$: ▵—$R_{\lambda }=200$, ▿—$R_{\lambda }=350$, ○—$R_{\lambda }=460$, and □—$R_{\lambda }=690$.