Kelvin-Helmholtz instability is an instability to be formed on the discontinuity of fluid velocity. For example, spiral shape observed in the Great Red Spot on the Jupiter is considered as this result.

[Initial Condition]

A discontinuity in both density and velocity between upper and lower fluids. Upper sky blue region is low density and moving to right with 0.5 times its sound speed. Lower orange region is high density and in the rest. The density ratio of two regions is 4.0. We add 10% perturbation of growing mode of the instability.

In the figure, color shows density, and arrows show velocity.

[Nonlinear Growth Stage]

The boundary of discontinuity starts surging as a sinusoidal wave and then grows into non-linear crests of waves.