A barotropic atmosphere is one in which changes in air density are driven solely by changes in pressure. It is a good approximation in the tropics, where horizontal temperature gradients are small. In a barotropic atmosphere, isobaric (uniform pressure) surfaces coincide with isopycnic (uniform air density) surfaces. From the ideal gas law, they must also coincide with isothermal (uniform temperature) and isentropic (uniform potential temperature) surfaces. Since there is no temperature gradient on isobaric surfaces, the geostrophic wind is independent of height (see (38) and (39)). Under adiabatic conditions (dθ/dt = 0), air parcels remain on isentropic surfaces, and since no pressure gradient exists along these surfaces to drive atmospheric motions, no potential energy is available for conversion into kinetic energy.
Outside the tropics, where meridional temperature gradients are large (Figure 11), the temperature varies along the isobars, and the atmosphere is said to be baroclinic. Isobars and isentropes do not coincide. In this case, pressure gradients can drive adiabatic displacement along isentropic surfaces. Conversion of potential energy into kinetic energy becomes possible. Temperature gradients along isobars cause vertical shear in the geostrophic wind (see thermal wind equation), leading to a strong jet stream in the upper troposphere as discussed in Section 7. The axis of the jet stream is located in the 30°–60° latitudinal band characterized by a pronounced meridional temperature gradient separating cold and dense air of polar origin from warmer, less dense tropical air. In the presence of strong velocity shears, the jet stream may be unstable with respect to small perturbations, and disturbances may amplify, producing the so-called baroclinic instability.
Figure 13 illustrates baroclinic instability. The meridional gradient in temperature causes the isentropic surfaces (isentropes) to slope upward with increasing latitude. A poleward motion at constant altitude or with an upward slope shallower than the isentropes produces an unstable atmosphere even though the isentropes imply a vertically stable atmosphere (∂θ/∂z > 0). Despite the stable conditions, potential energy from the flow can be converted into kinetic energy. Baroclinic instabilities drive the development of mid-latitude cyclones and associated frontal systems.
