Small-scale motions in turbulent boundary-free shear flows

Abstract

The present work is an experimental and numerical investigation of the small-scale motions in turbulent free-shear flows. In the far-field turbulence of a jet at high Reynolds number (Re? = 350) hot-wire anemometry (HWA) is applied to measure time series of flow velocity. By filtering these time series, large- and small-scale velocity fluctuations are obtained. Both the amplitude and the frequency of the small-scale signals are locally stronger (weaker) for positive (negative) fluctuations of the large-scale signal, which is refered to as amplitude and frequency modulation. The local amplitude and frequency of the small-scale signals increase monotonically with the strength of the large-scale velocity fluctuations. The same flow is also investigated with long-range ?PIV (microscopic Particle Image Velocimetry). The measurement is validated against the HWA signals by comparison of the turbulence statistics. A validation based on the topological content is also performed. The coherent structures of vorticity and of intense dissipation are adequately resolved, and their characteristic size is assessed. It is found that the size of the vortical structures does not change significantly when conditioned on strongly-positive or strongly-negative large-scale velocity fluctuations. Using the PIV results the amplitude and frequency modulation observed from HWA signals is explained as an inhomogeneous distribution of the small-scale structures within the flow. In particular, the analysis of ?PIV data reveals that the intense vortical and dissipation structures tend to be preferentially located in high-velocity regions, hence they are characterized by convection velocities higher than the mean velocity of the flow. Furthermore, the spatially resolved velocity vector fields allow to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25% of the value measured from hot-wire anemometry. The remaining 75% comes from the fixed spectral band filter used to obtain the large- and the small-scale signals, which does not consider the local convection velocity (Taylor hypothesis of frozen turbulence). A very similar overestimation of amplitude modulation when quantified in the time-frame is also confirmed analytically. Based on the experimental analysis on the jet an explanation for amplitude and frequency modulation is developed, which can be extended to other free-shear flows. The validity of this interpretation is assessed based on the analysis of Direct Numerical Simulations of a mixing layer, at the Reynolds number based on the Taylor microscale (Re? =) of 250. The local vorticity rms, taken as a measure of the small-scale activity, is found to be modulated by the large-scale velocity fluctuations depending on the position within the flow. In particular, on the low-speed side of the mixing layer, positive large-scale velocity fluctuations correspond to a stronger vorticity rms, whereas on the high-speed side, they correspond to a weaker vorticity rms. This is consistent with previous studies on a mixing layer. Important differences are found in the strength of the scale interaction from time series and in physical space, consistent with the predictions developed from the analysis of the jet. On the high-speed side of the mixing layer, amplitude modulation from time series largely underestimates the value obtained from spatial series, and overestimates it on the low-speed side. Therefore, the interaction between large-scale velocity fluctuations and small scales is dependent on the flow position within the mixing layer, similar to a turbulent boundary layer. Nonetheless, when the vorticity rms is correlated with the large-scale shear velocity gradients, the correlation coefficient is found to be nearly constant throughout the mixing layer, and close to unity. This reveals that the large and the small scales present a strong interaction independent of the position when the large-scale shear velocity gradients are considered, instead of the large-scale velocity fluctuations, as in the existing literature on amplitude modulation. The strong correlation between the large-scale gradients and the small scales suggests to investigate possible evidence of the so called “scale invariance” (Meneveau and Katz 2000). The alignment between the local vorticity and the large-scale vorticity is examined within the vortical tubes. It is found that the vorticity from unfiltered (representing the small scales) and from low-pass-filtered velocity vector fields (representing the larger scales) tend to be aligned within the vortical tubes. This suggests that the direction of vorticity does not vary significantly across the scales. Therefore, the anisotropy of the large scales is partially preserved at the small-scale level, which is in contrast with the Kolmogorov’s hypothesis of local isotropy.