 Kelvin–Helmholtz instability

For a planar vortex sheet separating equal-density streams of velocities $U_1$ and $U_2$, a mode of nonzero wavenumber $k$ has complex growth exponentOne sign has positive growth rate, so every nonzero wavenumber is unstable in the inviscid zero-thickness model.

Kelvin–Helmholtz instability (KHI) is a fluid dynamic phenomenon that occurs when there is a velocity shear in a continuous fluid medium. It arises when two fluid layers with different velocities interact, leading to the formation of waves and vortices at the interface between the layers. This instability can result in the mixing of the fluids and is characterized by the growth of perturbations at the interface.