Baroclinic instability is an instability relating to fluid dynamics.

Buoyancy forces can exist only in a fluid in which density varies on a surface of constant pressure. Such a fluid is called a baroclinic (literally, 'leaning pressure') fluid. The relative balance between Coriolis forces due to rotation and buoyancy forces determines whether the fluid is baroclinically stable or baroclinically unstable.

The concept of baroclinic instability helps to explain some important features of the so-called large scale waves in the mid-latitude atmosphere. These waves provide a mechanism for transporting heat and angular momentum and are believed to control the temperature gradient between the equator and the pole. The first accurate theoretical model to include baroclinic instability was the model developed by Jule Charney in 1947. He considered a simplified version of the equations of motion for the atmosphere in which the scaling is made for small Rossby number and a stratified fluid. The approximate equations are known as quasi-geostrophic system. In the Charney formulation the effect of the rotation of the earth is approximated by the so-called beta plane, in which the variation of the Coriolis parameter with latitude is approximated by a constant (traditionally symbolized by the Greek letter beta). A simplified version of the baroclinic instability was proposed independently by Eady in 1949. Eady considered constant vertical shear, no beta and an upper lid.

Baroclinic instability can be investigated in the laboratory using a rotating, fluid filled annulus. This is heated at the outer wall (think equator) and cooled at the inner wall (think pole) and the resulting fluid flows give rise to baroclinic waves.

The onset of baroclinic instability gives rise to a rich range of complex non-linear dynamics and has been the source of a large body of academic research over the last 50 years. Fluid dynamics | Atmospheric dynamics