Baroclinity

Density lines and isobars cross vertically in a baroclinic fluid.
Visualization of a (fictive) formation of isotherms (red-orange) and isobars (blue) in a baroclinic atmospheric layering.
A rotating tank experiment modelling baroclinic eddies in the atmosphere

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:

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.

  1. ^ Marshall, J., and R.A. Plumb. 2007. Atmosphere, Ocean, and Climate Dynamics. Academic Press,
  2. ^ Holton (2004), p. 77.
  3. ^ Gill (1982), p. 122: ″The strict meaning of the term ′barotropic′ is that the pressure is constant on surfaces of constant density...″
  4. ^ Tritton (1988), p. 179: ″In general, a barotropic situation is one in which surfaces of constant pressure and surfaces of constant density coincide; a baroclinic situation is one in which they intersect.″
  5. ^ Holton (2004), p. 74: ″A barotropic atmosphere is one in which density depends only on the pressure, , so that isobaric surfaces are also surfaces of constant density.″
  6. ^ Robinson, J. P. (1999). Contemporary climatology. Henderson-Sellers, A. (Second ed.). Oxfordshire, England: Routledge. p. 151. ISBN 9781315842660. OCLC 893676683.
  7. ^ Houze, Robert A. (2014-01-01), Houze, Robert A. (ed.), "Chapter 11 - Clouds and Precipitation in Extratropical Cyclones", International Geophysics, Cloud Dynamics, vol. 104, Academic Press, pp. 329–367, doi:10.1016/b978-0-12-374266-7.00011-1, ISBN 9780123742667