# Barotropy

(Redirected from Equation of barotropy)

## barotropy

The state of a fluid in which surfaces of constant density (
or temperature) are coincident with surfaces of constant pressure; it is the state of zero baroclinity.

Mathematically, the equation of barotropy states that the gradients of the density and pressure fields are proportional: where ρ is the density, p the pressure, and B a function of thermodynamic variables, called the coefficient of barotropy. With the equation of state, this relation determines the spatial distribution of all state parameters once these are specified on any surface. For a homogeneous atmosphere, B = 0; for an atmosphere with homogeneous potential temperature, where cv and cp are the specific heats at constant volume and pressure, respectively, R the gas constant, and T the Kelvin temperature; for an isothermal atmosphere, B = 1/(RT). It is not necessary that a fluid that is barotropic at the moment will remain so, but the implication that it does often accompanies the assumption of barotropy (
see autobarotropic). In this sense the assumption, or a modification thereof, is widely applied in dynamic meteorology. The important consequences are that absolute vorticity is conserved (to the extent that the motion is two dimensional), and that the geostrophic wind has no shear with height.
See equivalent barotropic model, barotropic vorticity equation, barotropic instability, barotropic disturbance.

Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . p. 77. 