Research

In this work, a complete physical picture of the vortex-pairing process is presented, including the instabilities and energy transfer involved in the process. We show that the hydrodynamic instabilities in initially laminar jets are more pronounced and trigger the transition to turbulence within the first two jet diameters. Linear stability theory is used to identify the fundamental frequency, and its dynamical importance in the vortex-pairing process is characterized. The subsequent nonlinear interactions between the fundamental and subharmonic are analyzed using the spectral turbulent kinetic energy budget. This analysis reveals that there is a backscatter of energy from the fundamental to its subharmonic. These findings provide evidence for Kelly's hypothesis (1967), demonstrating that there is an inverse energy cascade during vortex pairing.

Measurement data often contain partially missing or corrupted regions. For example, in particle image velocimetry (PIV) such measurements can result from shadowing, reflections from objects, irregular seeding,  and absence of sufficient number of tracer particles. Atmospheric data obtained via satellite imagery also suffer from partial obstruction due to cloud coverage. The estimation of the missing data is necessary for a complete characterization of the flow field.

In this work, we propose the gappy spectral proper orthogonal decomposition for reconstructing the missing data. The proposed gappy-SPOD method is fundamentally different from previous existing methods, in that it leverages both spatial and temporal coherence in estimating the compromised regions. The method accurately recovers the turbulence statistics as well as the missing instantaneous regions, even for a highly chaotic flow. It generally outperforms the established methods such as POD and Kriging, where it yields a significantly lower reconstruction error.

We extend spectral proper orthogonal decomposition (SPOD) for four different applications: low-rank reconstruction, denoising, frequency-time analysis, and prewhitening.  The primary utilities of these techniques are to extract the essential flow features and provide a low-dimensional representation of the data. To this end, we propose two approaches: ($i$) frequency-domain approach, which is a direct inversion of the SPOD algorithm, and ($ii$) time-domain approach, which is based on the oblique projection of the data onto the SPOD modes. The low-dimensional reconstructions from both approaches accurately capture the integral energy of the data. The former retains the monochromatic property and reconstructs the flow field associated with the necessary timescale, while the latter approach captures time-varying dynamics more accurately.  Building upon these approaches, we present a denoising strategy based on hard-thresholding of the SPOD eigenvalues. The proposed strategy achieves significant noise reduction while facilitating drastic data compression. Further, we propose a method for characterizing the intermittency of the spatially coherent flow structures. The distinctive feature of this method is that it indicates the time intervals during which a particular mechanism is active, thereby providing additional physical insight. 

Commercial and aviation aircraft generate excessive noise that can cause hearing loss. The high-speed fluid emerging from the exhaust of the engine nozzle forms an unstable shear layer that grows and rolls up into vortices that further pair up. These vortices , i.e., coherent structures are the sources of jet noise. The jet noise in the downstream direction is associated with large-scale coherent structures, whereas its source, in the sideline direction is debated. Few researchers associate the latter with small-scale turbulence, whereas others argue that large-scale structures are the source.

In this work, we extract the most energetic patterns of acoustic emissions to specific angles in the far field of subsonic, transonic, and supersonic jets. Using spectral proper orthogonal decomposition (SPOD), we trace the source location of the beams to the downstream, sideline, and upstream directions. A single superdirective acoustic beam dominates in the downstream direction. These beams emanate from the end of the potential core for low frequencies and the shear-layer region for higher frequencies. In the sideline direction, the acoustic patterns consist of beams that propagate upstream or perpendicular to the jet axis. The SPOD modes reveal that the sideline radiation originates from the same source locations as the dominant superdirective beams, which indicates that the sources of the sideline and downstream radiation are intimately linked. 

Turbulent wake studies have focused primarily on the vortex shedding (VS) mechanism. The VS mode is the most dominant coherent structure near the body and in the intermediate wake. In addition to this coherent structure, we demonstrate the existence of large-scale streaks – coherent elongated regions of streamwise velocity. Moreover, in the far wake, x/D≥70, these streaks become the energetically dominant coherent structure. To the best of our knowledge, this is the first study that reports the existence of streaks in turbulent wakes. 

The streamwise vortices lift up the low-speed fluid from the wake's core and push down high-speed fluid from the outer wake, forming streaks. Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake and that ejections contribute more than sweeps to events of intense negative Reynolds shear stress. Beyond the identification of streaks, we also explore the role of nonlinear interactions in the context of wakes. We find that the self-interaction of the VS mode generates the streamwise vortices at m=2, St→0, which leads to streak formation through the lift-up process.