3.1. Large-scale turbulence properties

The results in this section are obtained from the large-FOV measurements. We begin by considering the effect of the particles on the r.m.s. velocity fluctuations of the turbulence. Figure 3(a) shows the laden-to-unladen ratio for the horizontal component, $u_{1}'/u_{1,\varPhi =0}'$, for the different volume fractions. A monotonically increasing trend is apparent for both Stokes numbers, with the larger $St_{\eta }$ case displaying a stronger increase. The vertical component also increases with volume fraction, but less than the horizontal one. Indeed, the anisotropy ratio $u_{1}'/u_{3}'$ grows significantly over the considered range of volume fractions (figure 3b), the growth being again stronger for $St_{\eta } = 2.6$ than for $St_{\eta } = 0.3$.

Figure 3.

(a) The r.m.s. of the horizontal velocity fluctuation as a function of the particle volume fraction, normalized by the one measured in the unladen flow. (b) Ratio between the horizontal and the vertical r.m.s. fluctuations, as a function of the particle volume fraction. Squares indicate the $St_{\eta } = 2.6$ case, and circles indicate the $St_{\eta } = 0.3$ case. The data are from the large FOV.

The enhancement of the r.m.s. fluid velocity fluctuations in both directions indicates that the turbulent kinetic energy (TKE) is augmented significantly by the presence of the particles, as we will discuss later. Moreover, the fact that the particle-laden turbulence fluctuations are more intense in the horizontal than in the vertical direction is at odds with previous numerical studies: simulations of decaying (Ferrante & Elghobashi Reference Ferrante and Elghobashi2003) and forced (Bosse et al. Reference Bosse, Kleiser and Meiburg2006) homogeneous turbulence found that the addition of settling particles resulted in anisotropy ratios $u_{1}'/u_{3}'<1$. Also, the grid turbulence measurements of Geiss et al. (Reference Geiss, Dreizler, Stojanovic, Chrigui, Sadiki and Janicka2004) and Poelma et al. (Reference Poelma, Westerweel and Ooms2007) showed stronger fluid fluctuations in the direction of gravity than in the transverse direction. However, direct comparison with these experiments is hampered by the differences in parameters compared to the present case: the particles in Geiss et al. (Reference Geiss, Dreizler, Stojanovic, Chrigui, Sadiki and Janicka2004) were quasi-ballistic, while those in Poelma et al. (Reference Poelma, Westerweel and Ooms2007) were not small compared to the Kolmogorov scales, and produced wakes with large momentum deficit, which heavily impacted their weak decaying turbulence.

The influence of the settling particles on the large-scale turbulence properties is further illustrated by the integral scales, obtained from the spatial autocorrelation of the velocity fluctuations:

(3.1)\begin{equation} \rho_{ii}(\boldsymbol{r}) = \frac{\langle u_{i}(\boldsymbol{r})\,u_{i} (\boldsymbol{x}+\boldsymbol{r})\rangle}{\langle u_{i}(\boldsymbol{x})^{2}\rangle}, \end{equation}

where $x$ and $r$ are the position and separation vectors, respectively, and no index summation is implied. In general, the integral length scales associated with fluctuations $u_{i}$ over separations $r_{j}$ are defined as

(3.2)\begin{equation} L_{i,j} = \int_{0}^{r_{0}} \rho_{ii}(r_{j})\,{\rm d} r, \end{equation}

where $r_{0}$ is the first zero crossing of $\rho _{ii}$. In practice, the extent of the integration is limited by the size of the imaging window, and therefore we take as conventional estimate the separation at which the correlation function drops below 0.5. Other common methods such as extrapolating an exponential fit yield similar results. As in Carter & Coletti (Reference Carter and Coletti2017), we define the integral and transverse scales as $L_{L,1}=L_{1,1}$ and $L_{T,1}=L_{1,2}$, respectively. The subscript 1 indicates that we use the horizontal component of the velocity, the vertical one returning similar trends.

In figure 4(a), we show the autocorrelation of the horizontal velocity fluctuations along the horizontal separation, $\rho _{11}$, for the $St_{\eta } = 2.6$ case. The correlation decays faster with increasing volume fraction, which results in a drop of the longitudinal integral scale $L_{L,1}$ as shown in figure 4(b). As we already remarked, $u_{1}'$ increases with volume fraction, so the shrinking of the integral scale suggests that the falling particles subtract energy from the large scales and inject it at the small scales, with a positive global balance (i.e. a net increase of TKE). This view will be confirmed in the following sections.

Figure 4.

(a) Autocorrelation coefficient of the horizontal velocity fluctuations at the different volume fractions for $St_{\eta } =2.6$. (b) Corresponding longitudinal integral scale, normalized by the unladen case, as a function of the particle volume fraction. The data are from the large FOV.

To better appreciate the particle influence on the large-scale spatial structure of the turbulence, we plot in figure 5(a) the 0.5 contours of $\rho _{11}$ in the $(r_{1},r_{2})$-plane. With increasing volume fraction, the horizontal extent of the correlation area shrinks, decreasing $L_{L,1}$ as mentioned; instead, its vertical extent grows, increasing the transverse length scale $L_{T,1}$. This is quantified in figure 5(b), showing the $L_{L,1}/L_{T,1}$ ratio as a function of volume fraction. For the single-phase case, the ratio departs from the canonical value 2 due to incomplete homogeneity and isotropy across the FOV. The ratio shows a clear decreasing trend with increasing particle loading. The 0.5 contours of the vertical velocity autocorrelation $\rho _{22}$ (not shown for brevity) display a similar vertical stretch, with an increase of the longitudinal length scale ($L_{L,2} = L_{2,2}$) and decrease of the transverse length scale ($L_{T,2}=L_{2,1}$). Taken together, these results indicate that the energy-containing eddies become elongated vertically in the presence of falling particles at increasing concentrations. This contrasts with the above observation that the horizontal fluid fluctuations are excited more than the vertical ones: in single-phase turbulence, the integral scales are stretched in the direction along which fluctuations are more intense (Carter & Coletti Reference Carter and Coletti2017). The presence of the particles clearly alters the way energy is redistributed between different directions and across scales.

Figure 5.

(a) Contours of the autocorrelation coefficient $\rho _{11}$ in the two-dimensional scale space $(r_{1},r_{2})$ for the case $St_{\eta } = 2.6$ at different volume fractions. (b) Corresponding ratio between the longitudinal and transverse integral scales, as a function of the particle volume fraction. The data are from the large FOV.

3.2. Turbulent kinetic energy and dissipation rate

As anticipated in the previous subsection, the presence of particles in the present regime augments the turbulent kinetic energy of the carrier fluid. This is evident in figure 6, where we plot TKE calculated as

(3.3)\begin{equation} {\rm TKE} =\tfrac{1}{2}(2u_{1}^{'2} + u_{3}^{'2}) \end{equation}

from the large- and small-FOV data at different volume fractions. In (3.1), we assume that the out-of-plane velocity variance is equal to the measured horizontal component. This is expected when the baseline single-phase turbulence is approximately isotropic, which is justified by the value of $u_{1}'/u_{3}'$ in absence of particles (table 1). The change in TKE compared to the single-phase flow is marginal for $\varPhi _{v}\approx 10^{-6}$, in agreement with the order-of-magnitude estimate of Elghobashi (Reference Elghobashi1994). The turbulence is augmented monotonically with increasing volume faction, leading to TKE increases of 70 % at $\varPhi _{v} = 4\times 10^{-5}$ for $St_{\eta } = 0.3$, and more than 150 % at $\varPhi _{v}= 5\times 10^{-5}$ for $St_{\eta } = 2.6$. Such a dramatic augmentation of turbulence is in stark contrast with the criterion of Gore & Crowe (Reference Gore and Crowe1991) and with several previous experimental studies: Paris (Reference Paris2001), Hwang & Eaton (Reference Hwang and Eaton2006a,Reference Hwang and Eatonb) and Tanaka & Eaton (Reference Tanaka and Eaton2008) found that solid particles attenuated air turbulence. Those authors, however, considered significantly more inertial particles ($St_{\eta } \approx 50\unicode{x2013}100$), and in the following we reason that this is the likely cause of the different behaviour.

Figure 6.

Turbulent kinetic energy normalized by the unladen case, as a function of the particle volume fraction. Squares indicate the $St_{\eta }= 2.6$ case, and circles indicate the $St_{\eta } = 0.3$ case. The data are from the small FOV.

The increase in TKE is related to the energy balance in the particle-laden turbulence, where gravitational settling plays a major role: as the particles fall, they transfer potential energy into the flow. Following Hwang & Eaton (Reference Hwang and Eaton2006a), we consider the steady-state energy budget

(3.4)\begin{equation} E_{j} + E_{g} = \epsilon + \epsilon_{p}, \end{equation}

where the left-hand and right-hand sides represent the energy per unit time, and mass injected and dissipated in the fluid control volume, respectively. Here, $E_{j}$ is the forcing from the jets, which is independent of the mass loading and equals the energy dissipation rate in the single-phase cases. The energy per unit time released by the falling particles is $E_{g} = \varPhi _{m} \langle U_{3,p} \rangle g$, analogous to estimates for rising bubbles (Riboux, Risso & Legendre Reference Riboux, Risso and Legendre2010; Risso Reference Risso2018). The viscous dissipation of turbulence energy due to the cascade from larger to smaller eddies, $\epsilon$, is estimated by evaluating directly the in-plane velocity gradients resolved by PIV from the small FOV (see De Jong et al. Reference De Jong, Cao, Woodward, Salazar, Collins and Meng2009; Carter et al. Reference Carter, Petersen, Amili and Coletti2016). For single-phase turbulence in this facility imaged with similar parameters, such a direct estimate was shown to agree closely with the one based on velocity structure functions (Carter et al. Reference Carter, Petersen, Amili and Coletti2016; Carter & Coletti Reference Carter and Coletti2017, Reference Carter and Coletti2018). The presence of the particles leads to an extra dissipation $\epsilon _{p}$ associated with their interaction with the fluid, in particular the boundary layer around the particles, which is far below the PIV resolution limits. This can be estimated with the classic expression proposed by Elghobashi & Abou-Arab (Reference Elghobashi and Abou-Arab1983) and used in several later studies (Rogers & Eaton Reference Rogers and Eaton1991; Kulick et al. Reference Kulick, Fessler and Eaton1994; Hwang & Eaton Reference Hwang and Eaton2006a; Sahu, Hardalupas & Taylor Reference Sahu, Hardalupas and Taylor2016; among others):

(3.5)\begin{align} \epsilon_{p} &= \frac{\langle C \rangle}{\rho_{f}\tau_{p}}\,(\langle u_{i,fp}u_{i,fp} \rangle - \langle u_{i,fp}u_{i,p} \rangle) + \frac{1}{\rho_{f}\tau_{p}}\,(\langle cu_{i,fp}u_{i,fp} \rangle - \langle cu_{i,fp}u_{i,p} \rangle) \nonumber\\ &\quad +\frac{1}{\rho_{f}\tau_{p}}\,(\langle U_{i,fp} \rangle - \langle U_{i,p} \rangle) \langle cu_{i,fp} \rangle. \end{align}

Here, $C$ and $c$ correspond to the local particle concentration and the local particle concentration fluctuation, and $u_{fp}$ is the fluid velocity fluctuation at the particle location.

Figure 7(a) shows $\epsilon _{p}$ as a function of volume fraction (normalized by the unladen turbulence dissipation, $\epsilon _{\varPhi =0}$) evaluated in two ways: indirectly from (3.4) as $E_{j} + E_{g} - \epsilon$, and directly from (3.5). The results are displayed for $St_{\eta } = 2.6$, the outcome for $St_{\eta } = 0.3$ being analogous. Both methods show a similar trend, although with discrepancies at higher loadings. We remark that an accurate evaluation of $\epsilon _{p}$, following either method, is highly challenging for several reasons. First, the evaluation of $\epsilon$ in presence of suspended particles is even more difficult than in unladen turbulence (where it is already notoriously difficult). Second, (3.4) is based on the assumption that the forcing from the jets is independent of the presence of the particles, while the latter could indirectly influence the amount of kinetic energy injected at large scales in the investigated region. Third, and perhaps most important, (3.5) is based on the same assumptions as two-way-coupled point-particle models (Hwang & Eaton Reference Hwang and Eaton2006a), which have well-known shortcomings resulting in epistemic uncertainties that are hard to quantify. Indeed, the error bars representing statistical variability are not displayed for $\epsilon _{p}$ based on (3.5), as this is not the main source of error. Despite those limitations, both estimates of $\epsilon _{p}$ in figure 7(a) lead to a clear observation: at the larger considered volume fractions, the extra dissipation due to the particles becomes of the order of the baseline dissipation. Likewise, the energy input $E_{g}$ associated with gravitational settling, shown in figure 7(b) for the same case, also increases with $\varPhi _{v}$ and becomes comparable to $\epsilon _{\varPhi =0}$. The increase is due not only to the mass loading itself, but also to the mean settling velocity, which grows by $110\,\%$ over the considered range of volume fractions. This may be due to collective drag effects (as indicated by Bosse et al. Reference Bosse, Kleiser and Meiburg2006) or preferential sweeping (which was shown to remain important in recent two-way-coupled simulations by Tom, Carbone & Bragg Reference Tom, Carbone and Bragg2022). The analysis of the settling enhancement is beyond the scope of the present work and will be addressed in detail in a separate study. The important observation is that gravitational settling contributes majorly to the amount of energy injected and dissipated in the fluid per unit time. Whether TKE also increases is related to the time scale over which the dissipation is expressed. Tanaka & Eaton (Reference Tanaka and Eaton2010) pointed out how both the turbulence integral time scale and the particle response time may be appropriate candidates. The latter does not vary with the particle loading, while the former (taken as $L_{L}/u'$, averaging between horizontal and vertical components) increases by at most ${\approx }30\,\%$ for the higher $\varPhi _{v}$. Thus, as the time scale is not drastically changed by the presence of the particles, at steady state we can expect the turbulent kinetic energy of the system to rise with particle loading, as observed.

Figure 7.

(a) Particle-induced dissipation $\epsilon _{p}(a)$, and (b) gravitational energy input rate $E_{g}(b)$, both normalized by the turbulent dissipation of the unladen flow, for $St_{\eta }= 2.6$. In (a), upward-pointing triangles and downward-pointing triangles represent estimates of $\epsilon _{p}$ from (3.5) and (3.4), respectively. The data point from (3.5) at the highest concentration was discarded, due to the uncertainty in estimating the high-order terms. The data are from the small FOV.

This type of reasoning was used by Hwang & Eaton (Reference Hwang and Eaton2006a) to argue that settling contributed to augmenting turbulence also in their system; but that was not sufficient to offset the ability of their quasi-ballistic particles to act as sinks of fluid momentum. Their microgravity experiments (Hwang & Eaton Reference Hwang and Eaton2006b) confirmed such an argument, showing larger turbulence attenuation compared to an equivalent particle-laden turbulence regime under terrestrial gravity. Recently, Saito et al. (Reference Saito, Watanabe and Gotoh2019) used two-way coupled simulations to show that massively inertial point-particles (akin to fixed obstacles in the flow) severely attenuated turbulence, while the effect was much weaker for less inertial particles that more closely follow the flow. According to such a view, the difference between the present observations and those from Eaton and co-workers (Paris Reference Paris2001; Hwang & Eaton Reference Hwang and Eaton2006a,Reference Hwang and Eatonb; where $St_{\eta } \approx 50\unicode{x2013}100$) can be attributed to the smaller Stokes number in our system. Indeed, the one previous experimental study with solid particles in air at $St_{\eta }={O}(1)$ also found turbulence augmentation (Yang & Shy Reference Yang and Shy2005).

The natural question is why the settling of $St_{\eta }={O}(1)$ particles excites turbulence more than the settling of quasi-ballistic ones. A possible explanation is suggested by a comparison with bubble-laden turbulence. Mazzitelli et al. (Reference Mazzitelli, Lohse and Toschi2003a,Reference Mazzitelli, Lohse and Toschib) found numerically that small rising bubbles accumulate in the downward side of turbulent eddies due to the lift force (as recently confirmed experimentally by Salibindla et al. Reference Salibindla, Masuk, Tan and Ni2020), transferring momentum upwards, which enhances their ability to modify the turbulence. Likewise, small heavy particles with $St_{\eta }={O}(1)$ form clusters that oversample downward regions of the flow (Wang & Stock Reference Wang and Stock1993; Baker et al. Reference Baker, Frankel, Mani and Coletti2017; Petersen et al. Reference Petersen, Baker and Coletti2019), and therefore they may locally enhance turbulent fluctuations more effectively than ballistic particle that do not cluster. This interpretation is consistent with the larger TKE increase for particles with $St_{\eta }>1$, which experience stronger clustering than those with $St_{\eta }<1$ under the action of gravity (Matsuda, Onishi & Takahashi Reference Matsuda, Onishi and Takahashi2017; Petersen et al. Reference Petersen, Baker and Coletti2019).

As mentioned in the Introduction, although numerous authors investigated two-way coupling of point-particles, only a few of them included gravity in forced homogeneous turbulence. Bosse et al. (Reference Bosse, Kleiser and Meiburg2006) found turbulence attenuation by particles with $St_{\eta } \approx Sv_{\eta }\approx 1$, while Frankel et al. (Reference Frankel, Pouransari, Coletti and Mani2016) considered faster falling particles ($St_{\eta }=1.6$ and $Sv_{\eta }=6.8$) and reported an increase of TKE consistent with our observations. Besides the limitations of the point-particle approach, these comparisons with simulations also support the view that gravitational settling enhances the turbulence activity in the carrier flow.

3.3. Turbulence modification across scales

The change in TKE is the result of turbulence modification over the entire spectrum. Figure 8 shows the longitudinal second-order velocity structure function, which, compared to the Fourier spectrum, is less sensitive to finite-sample biases (Rensen et al. Reference Rensen, Luther and Lohse2005; De Jong et al. Reference De Jong, Cao, Woodward, Salazar, Collins and Meng2009) and to missing data that may result from the presence of particles (Poelma & Ooms Reference Poelma and Ooms2006). We consider the second-order structure function

(3.6)\begin{equation} D_{ii}(\boldsymbol{r}) = \langle[u_{i}(\boldsymbol{x}+ \boldsymbol{r}) - u_{i}(\boldsymbol{x})]^{2}\rangle, \end{equation}

where $\boldsymbol {x}$ is the position vector, and $\boldsymbol {r}$ is the separation vector. We focus on the longitudinal structure functions, where the velocity component is parallel to the separation vector, particularly on $D_{11}(r_{1})$, $D_{22}(r_{2})$ and the transverse structure functions showing the same behaviour. According to Kolmogorov theory (Kolmogorov Reference Kolmogorov1941), (3.6) scales as $(\epsilon r)^{{2}/{3}}$ for separations in the inertial range. Although the considered range of $Re_{\lambda }$ possesses limited scale separation, Carter et al. (Reference Carter, Petersen, Amili and Coletti2016) and Carter & Coletti (Reference Carter and Coletti2017) showed, and the present data confirm, that the single-phase turbulence in this facility approximately follows Kolmogorov scaling in the range $r \approx 20\eta \unicode{x2013} 50\eta$. The addition of particles alters this picture profoundly. In keeping with the pivoting effect, the energy becomes more evenly distributed across the scales as the particle loading increases: the dispersed phase intercepts part of the fluid momentum at the large scales, and injects it back into the fluid at small scales. The effect is already visible for $St_{\eta } = 0.3$ and is apparent for $St_{\eta } = 2.6$.

Figure 8.

Longitudinal second-order structure functions of the $u_{1}$ component for the different volume fractions for (a) $St_{\eta } = 0.3$ and (b) $St_{\eta } = 2.6$. The dashed line indicates the $r^{2/3}$ scaling predicted by Kolmogorov (Reference Kolmogorov1941) in the inertial range. The data are from the small FOV.

The cross-over separation $r_{c}$, i.e. the separation corresponding to the pivoting point, does not vary significantly with $\varPhi _{v}$, and lies in the ranges $30\eta$–$40\eta$ and $40\eta$–$50\eta$ for the lower and higher $St_{\eta }$, respectively. This difference could be a $St_{\eta }$ effect or a $Re_{\lambda }$ effect. The latter would be consistent with the proposal of Sundaram & Collins (Reference Sundaram and Collins1999) that $r_{c}$ scales with $\lambda$, while the former is at odds with the notion that $r_{c}$ decreases with $St_{\eta }$ (Poelma & Ooms Reference Poelma and Ooms2006). This conclusion, however, was based on simulations neglecting gravity, which here is crucial to the two-way coupling. Determining a specific trend for $r_{c}$ would require further measurements with different $Sv_{\eta }$ and a broader range of $St_{\eta }$. We do note that the range of scales where the fluctuating fluid energy is increased roughly corresponds to the size of the particle clusters in this regime (Petersen et al. Reference Petersen, Baker and Coletti2019).

Finally, the redistribution of the turbulent energy with increasing particle loading can be appreciated by considering the nonlinear inter-scale energy transfer rate, $\varPi$. Starting from the Kármán–Howarth–Monin equation (Monin, Yaglom & Lumley Reference Monin, Yaglom and Lumley1975), we recently performed such an analysis for the single-phase turbulence in this same facility (Carter & Coletti Reference Carter and Coletti2018; see also Lamriben, Cortet & Moisy Reference Lamriben, Cortet and Moisy2011; Gomes-Fernandes, Ganapathisubramani & Vassilicos Reference Gomes-Fernandes, Ganapathisubramani and Vassilicos2015; Portela, Papadakis & Vassilicos Reference Portela, Papadakis and Vassilicos2017; among others). Briefly, given two points $\mathbf {x}$ and $\mathbf {x}^{\prime \prime }$ associated with velocity fluctuations $u_{i}$ and $u_{i}^{\prime \prime }$ and separated by $\mathbf {r}$, one considers the difference $\delta u_{i} = u_{i} - u_{i}^{\prime \prime }$ and the associated energy $\delta q_{i} =\delta u_{i}\delta u_{i}$. (Assuming small-scale axisymmetry, as in Carter & Coletti (Reference Carter and Coletti2018), or isotropy leads to similar values and analogous conclusions.) The radial component of the nonlinear inter-scale energy transfer rate, $\varPi _{r} = \frac {1}{4}[({\partial }/{\partial r})(\langle \delta u_{i}\,\delta q_{i}^{2}\rangle r_{i}/r) + 1/r^{2} \langle \delta u_{i}\,\delta q_{i}^{2} \rangle r_{i}]$, is the only one making a net contribution in spherical coordinates. Thus, over the inertial range in single-phase turbulence, the average of $\varPi _{r}$ across all orientations in scale space is expected to balance the two-point kinetic energy dissipation $\epsilon _{r}$ (which in the present homogeneous flow coincides with the standard dissipation $\epsilon$). This is confirmed in figure 9, where the ratio $\varPi _{r}/\epsilon _{\varPhi =0}$ is plotted as a function of $r$ for $St_{\eta } = 2.6$. The negative sign of $\varPi _{r}$ indicates the expected direction of the energy cascade from larger to smaller scales, and the values of the ratio close to $-1$ for $r/\eta \approx 20\unicode{x2013}100$ reflect the $\varPi \unicode{x2013}\epsilon$ equilibrium in the inertial range of the unladen turbulence. With increasing particle loading, the magnitude of $\varPi _{r}$ in the same range grows significantly. This indicates that with increasing loading, the energy injected at the large scales is being transferred more effectively down the spectral pipeline towards the smaller scales. On the one hand, this is consistent with the observation that particles cause the energy to pivot towards a more even distribution across all scales, as illustrated in figure 8. On the other hand, it points to a specific mechanism by which such redistribution is realized, i.e. the enhancement of the energy cascade. The precise dynamics by which this is realized (e.g. by clusters accelerating the breakdown of large eddies, rather than high-concentration sheets causing instabilities; Kasbaoui, Koch & Desjardins Reference Kasbaoui, Koch and Desjardins2019) remains to be clarified, but it is likely specific to the present regime. In fact, particle-resolved DNS (PR-DNS) from Schneiders et al. (Reference Schneiders, Meinke and Schröder2017) found that Kolmogorov-scale particles dampened the inter-scale energy flux in the absence of gravity.

Figure 9.

Nonlinear inter-scale energy transfer rate, normalized by the turbulent dissipation and plotted as a function of the scale separation $r$, at the different particle volume fractions and for the $St_{\eta } = 2.6$ case. The dissipation from the unladen case is used to normalize all line plots; using $\epsilon$ from the individual particle-laden cases corroborates the observed trend of inter-scale transfer increasing with volume fraction. The data are from the small FOV.

In this multi-scale and two-way coupled system, the question of the inter-scale energy transfer is complex, and other interpretations of the results are possible. For example, the enhancement of $\varPi _{r}$ might be seen as a mere consequence of the energy added to the fluid by the falling particles, rather than by an intensification of the cascade. In such a scenario, however, one would expect a scale-independent shift of the energy spectrum, as opposed to the observed pivoting. Likewise, the increase of fluctuating energy at small scales could be due solely to the local action of the particles. If this were the case, however, such energy augmentation would be limited to scales much smaller than the range that appears affected. In conclusion, the present interpretation appears consistent with the ensemble of the experimental observations, but further data and analysis are required to make it more conclusive.