baroclinicity

Baroclinicity is the misalignment of the density of a fluid and its gradient of pressure. The term is used for the presence of this property and for a measure of it, which is proportional to:

∇p × ∇ρ

i.e., the sine of the angle between the surfaces of constant pressure (p) and constant density (ρ), and when they are aligned (when the above value is zero) there is no baroclinicity, a state termed barotropy. Baroclinic instability is instability of an atmosphere of a rotating planet due to baroclinicity. Baroclinic instability is the source of much weather phenomena such as cyclones, and also is considered a means by which protoplanetary disks affect planetary migration. A baroclinic atmosphere is an atmosphere where density depends upon both temperature and pressure whereas a barotropic atmosphere is one where density depends only upon pressure. In Earth weather in general, baroclinicity is found at boundaries between air masses (fronts) and barotropy is found within the air masses.