Sensitivity of vortex pairing and mixing to initial perturbations in stratified shear flows

The effects of different initial perturbations on the evolution of stratified shear flows that are subject to Kelvin-Helmholtz instability and vortex pairing have been investigated through direct numerical simulation. The effects of purely random perturbations of the background flow are sensitive to the phase of the subharmonic component of the perturbation that has a wavelength double that of the Kelvin-Helmholtz instability. If the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode is optimal, or close to it, then vortex pairing occurs. Vortex pairing is delayed when there is a phase difference, and this delay increases with increasing phase difference. In three-dimensional simulations vortex pairing is suppressed if the phase difference is sufficiently large, reducing the amount of mixing and mixing efficiency. For a given phase difference close enough to the optimal phase, the response of the flow to eigenfunctions perturbations is very similar to the response to random perturbations. The phase difference has a more significant effect on vortex pairing compared to the initial perturbation amplitude ratio between the KH and the subharmonic modes. In addition to traditional diagnostics, we show quantitatively that a nonmodal Fourier component in a random perturbation quickly evolves to be modal and describe the process of vortex pairing using Lagrangian trajectories.