A barotropic atmosphere is one in which the density depends only on the pressure, so that isobaric surfaces are also surfaces of constant density. The isobaric surfaces will also be isothermal, hence (from the thermal wind equation) the geostrophic wind is independent of height. Hence the motions of a rotating barotropic fluid are strongly constrained.
The structure of the barotropic mode is independent of depth and stratification.
Barotropic instability of an azimuthal jet in a rotating annulus was studied experimentally by Solomon et al.
Kuo (1978) performed a barotropic instability calculation for a cosine jet and observed that it is most unstable to barotropic perturbations (which have no vertical variation).
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