  This paper exposes a novel exploratory formalism, which end goal is the
numerical simulation of the dynamics of a cloud of particles weakly or strongly
coupled with a turbulent fluid. Giventhe large panel of expertise of the list
of authors, the content of this paper scans a wide range of connexnotions, from
the physics of turbulence to the rigorous definition of stochastic processes.
Our approachis to develop reduced-order models for the dynamics of both
carrying and carried phases which remainconsistant within this formalism, and
to set up a numerical process to validate these models. Thenovelties of this
paper lie in the gathering of a large panel of mathematical and physical
definitionsand results within a common framework and an agreed vocabulary
(sections 1 and 2), and in somepreliminary results and achievements within this
context, section 3. While the first three sections havebeen simplified to the
context of a gas field providing that the disperse phase only retrieves
energythrough drag, the fourth section opens this study to the more complex
situation when the dispersephase interacts with the continuous phase as well,
in an energy conservative manner. This will allowus to expose the perspectives
of the project and to conclude.
