Barotropic instability

Barotropic instability is a hydrodynamic instability that extracts kinetic energy from a horizontally sheared mean flow and deposits it into growing wave perturbations. It is the primary mechanism by which atmospheric Rossby waves amplify into the large-amplitude meanders of the jet stream, and it operates in the absence of vertical wind shear — hence the name 'barotropic,' from the Greek for weight and the condition of constant density surfaces.

The instability was first analyzed by John Charney in 1947 and independently by Eric Eady, though the specific barotropic formulation had been anticipated by Lord Rayleigh's work on the instability of inviscid shear flows. The necessary condition for barotropic instability, derived from the conservation of potential vorticity, requires that the meridional gradient of potential vorticity must change sign somewhere within the flow. This is the barotropic analogue of the Rayleigh inflection-point theorem: a flow with a monotonic potential vorticity profile is stable to horizontal perturbations.

In the real atmosphere, pure barotropic instability is rare. The jet stream is simultaneously barotropically unstable (through horizontal shear) and baroclinically unstable (through vertical shear and temperature gradients). The two instabilities interact nonlinearly: baroclinic instability generates the synoptic-scale waves that then undergo barotropic deformation and breaking, redistributing potential vorticity and shaping the large-scale circulation. The distinction between barotropic and baroclinic instability is therefore not a clean separation of mechanisms but a decomposition of the total energy source into horizontal and vertical components.

The concept of barotropic instability has been extended to oceanic flows, where it explains the growth of mesoscale eddies from horizontally sheared currents like the Gulf Stream and the Kuroshio. These eddies are the ocean's analogue of atmospheric storms: they transport heat, momentum, and tracer properties across ocean basins, and they dominate the kinetic energy of the ocean circulation at scales of 50–300 kilometers.