Large-scale streaky structures in turbulent jets

Abstract

Streaks have been found to be an important part of wall-turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a Mach 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry (PIV) taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor’s hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is approximately 15. The data were further analysed using SPOD, resolvent and transient growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics.

Resolvent-based analysis of streaks in turbulent jets

“…However, if the optimal forcing has a gain much larger than suboptimal ones, flow fluctuations are dominated by the optimal response [20,25]; thus, resolvent analysis has been useful in the determination of the underlying mechanisms in wall-bounded [15,17] and free-shear flows [20][21][22]26], encouraging the application of the method for this flow to better understand the role of the lift-up effect in a turbulent jet. The SPOD-mode energies for the first 4 modes is shown in figure 1(a), showing a dominance of the first mode in the low azimuthal wavenumber region, with the difference between optimal and suboptimal decreasing as we shift to higher values of m. This dominance is usually related to a preeminence of a physical mechanism (such as the Kelvin-Helmhotlz instability or the lift-up effect); in [11], the same dominance was identified for St = 0, with gains peaking at m = 3. Further analysis led to the conclusion that the coherent structure related to that peak was a low-azimuthal wavenumber streak.…”

“…We now focus on the analysis of the shapes of the resolvent and SPOD modes. For that, three wavenumbers were chosen as representative of the phenomenon we want to analyse: m = 3 is the peak wavenumber of streaks for this turbulent jet (from [11]); m = 7; 10 are wavenumbers whose SPOD modes have higher amplitudes in the region upstream of the jet; also, the streaky behaviour of the disturbances is clearer for these last cases. The shape of the streamwise component of the two first SPOD modes for these wavenumbers can be seen in figure 3.…”

“…Farther from the wall, similar streaky structures are also observed; these are referred to as superstructures [9] and are also thought to result from a similar self-sustaining process [10]. Elongated streaky structures, similar to those ubiquitous in wall-bounded turbulence, have recently been found in turbulent jets [11], and their characteristics greatly ressemble superstructures found in turbulent boundary layers.…”

“…It is shown by [20] that the SPOD modes should match the resolvent modes if the non-linear forcing is white noise in space, which gives us ground for the comparison between these two analyses. The SPOD is applied to the same database studied in [11,24]. Dual-plane time-resolved stereoscopic particle image velocimetry (PIV) was used to obtain the cross-spectral matrix for each azimuthal wavenumber for a Re = 4.6 × 10 5 turbulent jet with Mach M = 0.4.…”

“…For instance, transient growth analysis [14], focuses on finding initial disturbance that will be most amplified in the flow, resulting in conclusions about the time evolution of these structures. Both analyses have been used in the identification of streaks in turbulent jets [11], using the locally parallel framework, focusing on streamwise wavenumber k x = 0. Global analysis, which considers disturbances varying in the streamwise direction, leads to results with valuable information about the evolution of streaks, and provides a framework for comparison with spectral proper orthogonal decomposition modes.…”