Comparing phase-space and phenomenological modeling approaches for Lagrangian particles settling in a turbulent boundary layer

Under the right circumstances, particles (such as sand, dust, pollen, or water droplets) settling through the lowest 100 meters of the atmospheric boundary layer can experience a net enhancement in their average settling velocity due to their inertia. Since this enhancement arises from their interactions with the surrounding turbulence it must be modelled at coarse scales. Exact phase space methods can be used to model the physical mechanisms responsible for the enhanced settling, and these individual mechanisms themselves can be estimated or modelled to build a more general parameterization of the enhanced settling of inertial particles. In this presentation, we will describe recent work focused on using DNS data of a turbulent boundary layer coupled to Lagrangian point particles to estimate profiles of a drift-diffusion based parameterization of the fluid velocity sampled by the settling particles, which is key for determining the settling velocity enhancement of particles with low to moderate Stokes number. Our goal is to use these profiles to evaluate the efficacy of phenomenological modelling approaches for the enhanced settling velocity of inertial particles for particles with varying friction Stokes numbers and settling velocity parameters. We show that by increasing the settling velocity parameter at fixed moderate friction Stokes number, the drift component captures the increasing strength of Wang and Maxey's preferential sweeping mechanism, while the diffusion coefficient decreases due to the crossing trajectories mechanism. We then use these profiles to argue that the eddy-diffusivity-like closure commonly used in phenomenological models is incomplete, relying on inadequate empirical corrections. We will finish the talk with a brief discussion of opportunities for reconciling exact phase space approaches with simpler phenomenological approaches for use in coarse-scale weather models.