  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 (DNS). 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, vortex pairing occurs. Vortex paring 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 eigenvalues perturbations is very similar to the response to random
perturbations. In addition to traditional diagnostics, we show quantitatively
that a non-modal Fourier component in a random perturbation quickly evolves to
be modal and describe the process of vortex pairing using Lagrangian
trajectories.
