Baroclinity

In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the density depends on both temperature and pressure (the fully general case). A simpler case, barotropic flow, allows for density dependence only on pressure, so that the curl of the pressure-gradient force vanishes. Baroclinity is proportional to: which is proportional to the sine of the angle between surfaces of constant pressure and surfaces of constant density. Thus, in a barotropic fluid (which is defined by zero baroclinity), these surfaces are parallel. In Earth's atmosphere, barotropic flow is a better approximation in the tropics, where density surfaces and pressure surfaces are both nearly level, whereas in higher latitudes the flow is more baroclinic. These midlatitude belts of high atmospheric baroclinity are characterized by the frequent formation of synoptic-scale cyclones, although these are not really dependent on the baroclinity term per se: for instance, they are commonly studied on pressure coordinate iso-surfaces where that term has no contribution to vorticity production. Eady Model Baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and in the oceans. In the atmosphere it is the dominant mechanism shaping the cyclones and anticyclones that dominate weather in mid-latitudes. In the ocean it generates a field of mesoscale eddies (100 km or smaller) that play various roles in oceanic dynamics and the transport of tracers. Whether a fluid counts as rapidly rotating is determined in this context by the Rossby number, which is a measure of how close the flow is to solid body rotation. More precisely, a flow in solid body rotation has vorticity that is proportional to its angular velocity. The Rossby number is a measure of the departure of the vorticity from that of solid body rotation.