Inertial Effects on the Vertical Transport of Suspended Particles in a Turbulent Boundary Layer

In many atmospheric flows, a dispersed phase is actively suspended by turbulence, whose competition with gravitational settling ultimately dictates its vertical distribution. Examples of dispersed phases include snow, sea-spray droplets, dust, or sand, where individual elements of much larger density than the surrounding air are carried by turbulent motions after emission from the surface. In cases where the particle is assumed to deviate from local fluid motions only by its gravitational settling (i.e., they are inertialess), traditional flux balances predict a power-law dependence of particle concentration with height. It is unclear, however, how particle inertia influences this relationship, and this question is the focus of this work. Direct numerical simulations are conducted of turbulent open-channel flow, laden with Lagrangian particles of specified inertia; in this way the study focuses on the turbulent transport which occurs in the lowest few meters of the planetary boundary layer, in regions critical for connecting emission fluxes to the fluxes felt by the full-scale boundary layer. Simulations over a wide range of particle Stokes number, while holding the dimensionless settling velocity constant, are performed to understand the role of particle inertia on vertical dispersion. It is found that particles deviate from their inertialess behaviour in ways that are not easily captured by traditional theory; concentrations are reduced with increasing Stokes number. Furthermore, a similarity-based eddy diffusivity for particle concentration fails as particles experience inertial acceleration, precluding a closed-form solution for particle concentration as in the case of inertialess particles. The primary consequence of this result is that typical flux parametrizations connecting surface emission models (e.g., saltation models or sea-spray generation functions) to elevated boundary conditions may overestimate particle concentrations due to the reduced vertical transport caused by inertia in between; likewise particle emission may be underestimated if inferred from concentration measurements aloft.