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Home/Biophysics, Fluids & Geoscience/Kelvin–Helmholtz Shear Instability

Kelvin–Helmholtz Shear Instability

Kelvin–Helmholtz instability grows on a sheared interface between fluids when destabilizing inertia overcomes stabilizing effects such as surface tension or density stratification. The simulator shows a toy dispersion σ(k) and an interface built from a few growing Fourier modes for visualization only.

Who it's for: Fluid mechanics students needing a bridge between shear layers and billow clouds.

Key terms

  • Kelvin–Helmholtz
  • Shear instability
  • Dispersion relation
  • Surface tension

Live graphs

Shear & stabilization

2.2
0.08

Real Kelvin–Helmholtz growth depends on density difference, surface tension, and viscosity. Here σ(k) is a phenomenological curve: long waves grow when shear wins; short waves are damped by the “surface tension” term — use it to discuss selection of a dominant ripple scale.

Measured values

Fastest k (grid search)1.865
σ(k_max)1.0558

How it works

A cartoon of shear-driven wrinkling: superposed modes with growth rates from a simplified σ(k) kernel, plus the corresponding dispersion curve.

Frequently asked questions

Is σ(k) derived from the full two-fluid dispersion relation?
No. It is a compact phenomenological curve used to discuss band-pass growth: long waves feel shear, short waves are damped by the tension proxy.