Nonlinear dynamics of vortex pairing in transitional jets

This study investigates the onset of linear instabilities and their later nonlinear interactions in the shear layer of an initially laminar jet using high-fidelity simulations. We present a quantitative analysis of the vortex-pairing phenomenon by computing the spatial growth rates and energy budget of the dominant frequencies. Compared with a turbulent jet, the hydrodynamic instabilities and vortex pairing are enhanced in an initially laminar jet. Using local linear theory, we identify the fundamental as the frequency with the largest spatial growth rate, and its exponential growth causes the shear layer to roll up into vortices. Visualisations and conditional $x$ – $t$ plots reveal that fundamental vortices pair to form subharmonic vortices, which then merge to produce second subharmonic vortices. The energy transfer during this process is evaluated using the spectral turbulent kinetic energy equation, focusing on dominant coherent structures identified through spectral proper orthogonal decomposition. Spectral production and nonlinear transfer terms show that the fundamental frequency gains energy solely from the mean flow, while subharmonics gain energy both linearly from the mean flow and nonlinearly through backscatter from the fundamental frequency. Our results confirm Monkewitz’s theoretical model of a resonance mechanism between the fundamental and subharmonic, which supplies energy to the subharmonic. We highlight the energetic versus dynamical importance of tonal frequencies. The second subharmonic corresponds to the largest spectral peak, while the fundamental, though the fourth largest spectral peak, is dynamically dominant, as it determines all other spectral peaks and supplies energy to the subharmonics through a reverse energy cascade.