The impact of stable modes on the merging characteristics of Kelvin-Helmholtz vortices

The dynamics of vortices are ubiquitous in both hydrodynamics and MHD. The merging of vortices is especially relevant to shear-flow instabilities and the dynamics of magnetic islands in fusion devices. This study focuses on investigating the dynamics of vortex mergers in shear-flow (Kelvin-Helmholtz) instabilities. We examine the effect of the inclusion and exclusion of the conjugate stable mode to the unstable mode and the effect of varying the Reynolds number and the phase differences between the Fourier modes on the onset time for merger events. An emphasis is placed upon the relative difference between the phases of a given Fourier wavenumber and the wavenumber with half of that value (the first subharmonic) as this has been demonstrated by Guha and Rahmani (2019) to affect the merging time of vortices. The effect of the stable mode on the progression of vortex mergers has not been studied before. This work examines the importance of the stable mode and whether or not its contribution would have a non-negligible effect on vortex mergers in future studies of shear-flow driven instabilities. Furthermore, it is anticipated that the information gathered from this investigation will aid future endeavors that focus on the dynamics of magnetic islands or shear-flow instabilities.