Nonlinear energy transfer in vortex-pairing of initially-laminar jets*

In this study, we investigate the vortex-pairing process and its associated nonlinear energy transfer in the shear layer of an initially-laminar jet. Large-eddy simulations (LES) of a turbulent and initially-laminar jet are performed. Compared to the turbulent jet, the initially-laminar jet develops later but at a faster rate, resulting in a shorter potential core length and a hump in the RMS velocity along the centerline. The latter is caused due to the vortex-pairing in the shear layer. The vortex-pairing process involves two distinct occurrences: ($i$) two vortices of $St =1.76 $ pair to form an $St=0.88$ vortex, and ($ii$) two $St = 0.88$ vortices pair to form an $St=0.44$ vortex. Using local stability theory, we identify the fundamental as the most unstable frequency, which is $St=1.76$. Next, we evaluate the energy transfer between different frequencies, based on the nonlinear energy transfer term in the spectral turbulent kinetic energy equation. For this purpose, we employ bispectral mode decomposition (BMD), a technique that measures the intensity of triadic interactions. Our findings show that the energy is transferred from the fundamental to its subharmonic, resulting in the growth of the subharmonic. Additionally, energy transfer from the first subharmonic to its second subharmonic leads to the growth of the second subharmonic.  These energy transfers are primarily driven by two dominant triads, ($St_1,St_2,St_3$) = (1.76,-0.88,0.88), and (0.88,-0.44,0.44). Our results are consistent with previous work by citet{monkewitz1988subharmonic}, which demonstrated that the transfer was due to a resonance mechanism between the fundamental and subharmonic. The energy transfer during vortex-pairing exhibits characteristics of an inverse energy cascade.