Shear instability

A shear instability is growth of disturbances that draw kinetic energy from spatial variation of a base-flow velocity. The energy-transfer term involves the mean velocity gradient and perturbation velocity correlations. A velocity gradient alone does not guarantee instability: viscosity, stratification, boundaries and the profile shape matter. Kelvin-Helmholtz instability is a central interfacial example. For a smooth inviscid parallel shear flow, Rayleigh's inflection-point theorem makes an interior inflection point necessary for an exponentially growing two-dimensional normal mode; it is not sufficient. Applying this local parallel-flow criterion to a slowly varying boundary layer is a stability heuristic rather than a complete viscous stability calculation.