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

Statistical and probabilistic modeling of a cloud of particles coupled with a turbulent fluid