Stochastic model for the residence time of solid particles in turbulent Rayleigh-Bénard flow

Abstract

We take inspiration from the turbulent Rayleigh-B\`enard flow of the Pi Chamber and consider a particle-laden direct numerical simulation (DNS). The aim of our study is to develop a simple stochastic model that can accurately describe the residence times of the particles in the flow. The underlying conceptual picture is based on the repeated trips that particles take between the top and bottom boundaries, driven by the convective cells that occur in Rayleigh-B\`enard turbulence. Beyond demonstrating the model's efficacy, we use the framework to shed light on the independent roles that gravity and inertia play in governing residence times.