  Using two-dimensional simulations, we numerically explore the dependences of
Kelvin-Helmholtz instability upon various physical parameters, including
viscosity, width of sheared layer, flow speed, and magnetic field strength. In
most cases, a multi-vortex phase exists between the initial growth phase and
final single-vortex phase. The parametric study shows that the evolutionary
properties, such as phase duration and vortex dynamics, are generally sensitive
to these parameters except in certain regimes. An interesting result is that
for supersonic flows, the phase durations and saturation of velocity growth
approach constant values asymptotically as the sonic Mach number increases. We
confirm that the linear coupling between magnetic field and Kelvin-Helmholtz
modes is negligible if the magnetic field is weak enough. The morphological
behaviour suggests that the multi-vortex coalescence might be driven by the
underlying wave-wave interaction. Based on these results, we make a preliminary
discussion about several events observed in the solar corona. The numerical
models need to be further improved to make a practical diagnostic of the
coronal plasma properties.
