The impact of stable eigenmodes on the merging dynamics of Kelvin-Helmholtz vortices

The merging of vortices in instability-driven turbulence, an important aspect of vortex dynamics in hydrodynamic and MHD turbulence, is widely believed to be well-modeled by nonlinear interactions between unstable eigenmodes, with stable eigenmode dynamics typically being neglected. This assumption is re-evaluated as stable eigenmodes, conjugate to the Kelvin-Helmholtz (KH) unstable eigenmode, have been shown to be nonlinearly excited through mode coupling to amplitudes comparable to the unstable mode rather than vanishing. Here, we examine novel effects of the stable eigenmode on the onset and completion of KH vortex mergers. This is achieved by projecting hydrodynamic KH turbulence simulation data onto an inviscid linear eigenmode basis to isolate eigenmode effects. It is shown that unstable-stable eigenmode interactions are significantly more important than interactions between large and small length scales in merger dynamics and that the stable mode contribution is needed for the merger to occur. Excluding either the unstable or stable eigenmode leads to inaccuracies of the predicted merger time on the order of the instability e-folding time. 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.