Transport by waves and turbulence: Dilute suspensions in stably stratified plane Poiseuille flow

Abstract

We investigate the transport dynamics of negatively buoyant passive sediment in a thermally stratified plane Poiseuille flow using numerical simulation, exploring the influence of large-scale coherent structures on sediment transport processes. Sediment concentration fields are passively solved with settling velocities of $V_s = 0.005$, $V_s = 0.01$ and $V_s = 0.02$, made dimensionless by the friction velocity. Strong buoyancy forces in the core have a profound impact on sediment transport, leading to two-layer sediment concentration profiles with concentration gradients increasing with sediment settling velocity, $V_s$. When compared to unstratified flow, stratification leads to considerably larger differences in concentration profiles and higher order statistics between the three different sediments. When scalar statistics are appropriately scaled by either $\theta_\tau$ for temperature or $V_s \overline{c}$ for sediment, where $\theta_\tau$ is the thermal shear temperature and $\overline{c}$ is the vertically varying mean sediment concentration, scalar statistics collapse to near common vertical profiles. Collapse is explained by revisiting the gradient diffusion hypothesis, which links scalar fluxes to respective mean gradients. However, collapse of scalars is poor in the channel core where large concentration gradients coincide with large-scale mixing events. Here the differences between vertical turbulent diffusivities of sediment and temperature increase with increasing $V_s$, reaching 20% for $V_s = 0.02$. Discrepancies arise due to a breakdown of the linear gradient diffusion hypothesis. Predictions using the gradient diffusion hypothesis are expected to worsen with increasing settling velocity, indicating that classical models poorly predict dilute particle transport in strongly stratified flows, which are common in a range of environmental and industrial settings.