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