Baroclinity

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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.^[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.

Baroclinity is proportional to:

${\displaystyle \nabla p\times \nabla \rho }$

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.^[3][4][5]

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.^[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.