UC San Diego

Turbulent jets are canonical flows that occur when fluid emerges from an orifice into the surrounding environment, such as the jet from aircraft engines. As the fluid emerges from the nozzle, it forms an unstable shear layer that grows very rapidly, forming large-scale coherent structures, which are the main sources of aft-angle jet noise. The mechanism behind the generation of jet noise is still not fully understood. Further insights into characteristics of coherent structures can aid our understanding of turbulence, and in modeling and controlling various mechanisms. %The development of techniques for the education of coherent structures is another objective of this work.The main foci of this work are: (i) performing high-fidelity numerical simulations of turbulent jets and extracting physical insights from coherent flow structures, and (ii) developing techniques that extract these flow structures from the large dataset generated by these simulations.

In recent years, spectral proper orthogonal decomposition (SPOD) has emerged as a major tool for extracting coherent structures. In the first part, we extend SPOD for low-rank reconstruction, denoising, prewhitenening, frequency–time analysis, and gappy-data reconstruction. Two approaches for flow-field reconstruction are proposed, a frequency-domain approach, and a time-domain approach. A SPOD-based denoising strategy is also presented, which achieves significant noise reduction while facilitating drastic data compression. A convolution-based strategy is proposed for frequency-time analysis that characterizes the intermittency of spatially coherent flow structures. When applied to the turbulent jet data, SPOD-based frequency–time analysis reveals that the intermittent occurrence of large-scale coherent structures is directly associated with high-energy events. Lastly, a new algorithm, gappy-SPOD, is developed that leverages the space-time correlation of SPOD modes to estimate missing data. Even for highly chaotic flows with up to 20\% missing data, our method facilitates that structures associated with different time scales are well-estimated in the missing regions. For the cases considered here, it outperforms established techniques such as gappy-POD and Kriging.

In the second part, we investigate the nonlinear dynamics and controllability of coherent structures by actuating them. Large-eddy simulations (LES) of two unforced and four forced jets at $Re = 50,000$ and $M_j = 0.4$ were performed. The two unforced jets include an initially laminar and a turbulent jet. All four forced jets are turbulent and are forced at the azimuthal wavenumbers $m=0$, $m=\pm1$, $m=\pm2$, and $m=\pm6$. The unforced and forced jets were validated with companion experiments. Compared to the turbulent jet, the initially laminar jet develops later but at a faster rate, which is a result of the vortex pairing in the shear layer. The emphasis of the analysis is on characterizing the vortex pairing and the associated nonlinear energy transfer. Here, for the first time, we evaluate the spectral energy budget based on the leading modes of the SPOD. Our analysis reveals that energy flows from the fundamental to its subharmonic, resulting in the growth of the subharmonic. These results provide evidence for a previously suggested parametric resonance mechanism. In the forced jets, we examine the effect of forcing using a recently proposed method, bispectral mode decomposition (BMD), which extracts flow structures associated with nonlinear triadic interactions. We use BMD to construct a cascade of triads and find that the most dominant triads arise due to fundamental self-interaction and second-harmonic-fundamental difference interaction. Furthermore, our analysis of the far-field in the unforced and $m=0$-forced jets sheds light on the crucial role of difference-interactions in the generation of jet noise.