From AMS Glossary
The hydrodynamic instability arising from certain distributions of vorticity in a two-dimensional nondivergent flow.
This is an inertial instability in that kinetic energy is the only form of energy transferred between current and perturbation. The variation of vorticity in the basic current may be concentrated in discontinuities of the horizontal wind shear (to be distinguished from Helmholtz instability, where the velocity itself is discontinuous) or may be continuously distributed in a curved velocity profile. A well-known necessary condition for barotropic instability is that the basic state vorticity gradient must have both signs in the domain (i.e., counterpropagating Rossby waves must be possible).