Vertical dispersion of inertial particles in wall-bounded turbulence

The turbulent transport of scalars in wall-bounded turbulence is an important problem that has received a great deal of attention. Similarity theory suggests that the scalar concentration exhibits a logarithmic wall-normal profile, which implies that vertical scalar fluxes are uniform with height. An extension of this theory, begun by Rouse and Prandtl, includes when the particles are heavy, i.e. they experience gravitational settling towards the wall. In this scenario the upwards turbulent flux can come into balance with the downwards settling velocity, and what results is a concentration profile which obeys a power law with wall-normal distance whose exponent is often referred to as the Rouse number. In this study, we extend this problem to include the effects of particle inertia, and consider whether or not this similarity theory holds for particles which are not necessarily traveling with the local fluid velocity. Direct numerical simulation with Lagrangian point particles are used to test asymptotic extensions to the Prandtl/Rouse theory, and interpretations are offered on how to describe the flux-profile relationship of settling, inertial particles in wall-bounded turbulence.