Baroclinity
[1][2] 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.
[6] These midlatitude belts of high atmospheric baroclinity are characterized by the frequent formation of synoptic-scale cyclones,[7] 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.
In the atmosphere it is the principal mechanism shaping the cyclones and anticyclones that dominate weather in mid-latitudes.
[citation needed] In a compressible gas such as the atmosphere, the relevant measure is the vertical gradient of the entropy, which must increase with height for the flow to be stably stratified.
[citation needed] The strength of the stratification is measured by asking how large the vertical shear of the horizontal winds has to be in order to destabilize the flow and produce the classic Kelvin–Helmholtz instability.
[citation needed] Before the classic work of Jule Charney and Eric Eady on baroclinic instability in the late 1940s,[8][9] most theories trying to explain the structure of mid-latitude eddies took as their starting points the high Rossby number or small Richardson number instabilities familiar to fluid dynamicists at that time.
[citation needed] Baroclinic instability can be investigated in the laboratory using a rotating, fluid filled annulus.
In general, the evolution of vorticity can be broken into contributions from advection (as vortex tubes move with the flow), stretching and twisting (as vortex tubes are pulled or twisted by the flow) and baroclinic vorticity generation, which occurs whenever there is a density gradient along surfaces of constant pressure.
[citation needed] The study of the evolution of these baroclinic instabilities as they grow and then decay is a crucial part of developing theories for the fundamental characteristics of midlatitude weather.
Internal gravity waves as well as unstable Rayleigh–Taylor modes can be analyzed from the perspective of the baroclinic vector.
For example, in bodies of water, a gradual gradient in temperature or salinity is sufficient to support internal gravity waves driven by the baroclinic vector.
