A Reinterpretation of Phenomenological Modeling Approaches for Lagrangian Particles Settling in a Turbulent Boundary Layer

It has long been known that under the right circumstances, inertial particles (such as sand, dust, pollen, or water droplets) settling through the atmospheric boundary layer can experience a net enhancement in their average settling velocity due to their inertia. Since this enhancement arises due to their interactions with the surrounding turbulence it must be modelled at coarse scales. Models for the enhanced settling velocity (or deposition) of the dispersed phase that find practical use in mesoscale weather models are often ad hoc or are built on phenomenological closure assumptions, meaning that the general deposition rate of particles is a key uncertainty in these models. Instead of taking a phenomenological approach, exact phase-space methods can be used to model the physical mechanisms responsible for the enhanced settling, and these individual mechanisms can be estimated or modelled to build a more general parameterization of the enhanced settling of inertial particles. In this work, we use direct numerical simulations (DNS) and phase-space methods as tools to evaluate the efficacy of phenomenological modeling approaches for the enhanced settling velocity of inertial particles for particles with varying friction Stokes numbers and settling velocity parameters. We use the DNS data to estimate profiles of a drift-diffusion based parameterization of the fluid velocity sampled by the particles, which is key for determining the settling velocity behaviour of particles with low to moderate Stokes number. We find that by increasing the settling velocity parameter at moderate friction Stokes number, the magnitude of preferential sweeping is modified, and this behaviour is explained by the drift component of the aforementioned parameterization. These profiles indicate that that when eddy-diffusivity-like closures are used to represent turbulent transport, empirical corrections used in phenomenological models may be potentially compensating for their incompleteness. Finally, we discuss opportunities for reinterpreting phenomenological approaches for use in coarse-scale weather models in terms of the exact phase-space approach.