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Equatorial density enhancements (EDEs) are a very common astronomicalphenomenon. Studies of the circumstellar environments (CSE) of young stellarobjects and of evolved stars have shown that these objects often possess thesefeatures. These are believed to originate from different mechanisms, rangingfrom binary interactions to the gravitational collapse of interstellarmaterial. Quantifying the effect of the presence of this type of EDE on theobservables is essential for a correct interpretation of high-resolution data.We seek to investigate the manifestation in the observables of a circumstellarEDE, to assess which properties can be constrained, and to provide an intuitivebedrock on which to compare and interpret upcoming high-resolution data (e.g.\emph{ALMA} data) using 3D models. We develop a simplified analyticalparametrised description of a 3D EDE, with a possible substructure such aswarps, gaps, and spiral instabilities. In addition, different velocity fields(Keplerian, radial, super-Keplerian, sub-Keplerian and rigid rotation) areconsidered. The effect of a bipolar outflow is also investigated. Thegeometrical models are fed into the 3D radiative transfer code {\tt LIME}, thatproduces 3D intensity maps throughout velocity space. We investigate thespectral signature of the $J$=3$-$2 up to $J$=7$-$6 rotational transitions ofCO in the models, as well as the spatial aspect of this emission by means ofchannel maps, wide-slit position-velocity (PV) diagrams, stereograms, andspectral lines. Additionally, we discuss methods of constraining the geometryof the EDE, the inclination, the mass-contrast between the EDE and the bipolaroutflow, and the global velocity field. Finally, we simulated \emph{ALMA}observations...

Simplified models of circumstellar morphologies for interpreting high-resolution data. Analytical approach to the equatorial density enhancement