A three-part study is made of the development of vorticity patterns in the flow of inviscid, stratified fluids. The first part consists of a study of aspects of the hydrodynamic stability of swirling flows. Features of the instability mechanisms of two dimensional flow of a homogeneous fluid, for which circulation can take on the role of a pseudo-stratifier, and of a non-gravitating fluid possessing a radial density stratification are highlighted by seeking analytical solutions to the normal mode stability problem for particular basic flow configurations. The effect of a radial gravity field is then incorporated into the analysis and an indication given of the limited physical significance of this case to small scale cloud patterns in the earth's equatorial atmosphere. A study is also made of the stability of a baroclinic equatorial atmosphere to perturbations that are axi-symmetric with respect to the earth's axis of rotation. Part II is devoted to a study of the possible effects of stirring processes in rotating fluids. A survey of existing theories on this topic is presented, and a distinction drawn between mechanical stirring of a homogeneous fluid by an external agency and thermal stirring of a stratified fluid due to a hydro-thermodynamic instability. A heuristic model is developed to determine the form of the Reynolds stress induced by mechanical stirring, whilst Ertel's 'potential vorticity' theorem is employed to elucidate the quintessential properties of thermal stirring. In the last part of the work numerical integrations are performed to trace the time development of the initial distribution of sets of point vortices. The investigation is undertaken to obtain an increased understanding of the advective development of strong swirling motion in the two dimensional flow of a homogeneous fluid.