Kelvin-Helmholtz Instability

What you are seeing: two fluid layers sliding past one another at a sheared interface. The streamfunction $\psi = -\ln(\cosh y + A \cos x)$ generates the exact cats-eye flow as a function of the amplitude $A$ . As $A$ increases from 0, the interface rolls up into a row of vortices and the layers mix

Figure 1. Kelvin-Helmholtz cats-eye flow. Method: closed-form streamfunction + RK4 tracer advection.

Stuart A0.30

tracer count2000

animation speed2

show streamlineson

WHAT TO TRY

Raise the Stuart parameter A: the sheared interface rolls up into the classic Kelvin-Helmholtz cat-eye billows, the same vortices in cloud bands and on Jupiter.
Toggle the streamlines: the flow wraps around each vortex core, showing how the velocity shear feeds energy into the growing rollers.
Add more tracers: they get wound into spirals, visualizing how the instability mixes the two layers across what was a sharp shear line.