Slip velocity statistics of settling inertial particles in wall bounded turbulence*

In studies of the dispersion of large particles (such as coarse dust grains) in the atmospheric surface layer, knowledge of both the mean and fluctuating components of the turbulent drag (through the particle slip velocity) is key. In this work, we will highlight results from a series of coupled Eulerian-Lagrangian direct numerical simulations of wall bounded turbulent flows, wherein we identify the dominant mechanisms controlling the slip velocity variance. We utilize a statistical framework to derive continuum equations for the slip velocity variance of inertial settling Lagrangian particles in a turbulent boundary layer. We find that depending on the parameter regime of the particles, the slip variance is primarily controlled by local differences between the “seen" variance and the particle velocity variance, while terms appearing due to the inhomogeneity of the turbulence are sub-leading until the settling parameter becomes large.

We compare the results to a recently developed model of the slip velocity variance in homogeneous turbulence and find that while there is good agreement for low values of the settling parameter, systematic errors remain, possibly due to implicit non-local effects arising from rapid particle settling and inhomogeneous turbulence.