New guidelines for the application of Stokes' models to the sinking velocity of marine aggregates

Abstract

Numerical simulations of ocean biogeochemical cycles need to adequately represent particle sinking velocities (SV). For decades, Stokes' Law estimating particle SV from density and size has been widely used. But while Stokes' Law holds for small, smooth, and rigid spheres settling at low Reynolds number, it fails when applied to marine aggregates complex in shape, structure, and composition. Minerals and zooplankton can alter phytoplankton aggregates in ways that change their SV, potentially improving the applicability of Stokes' models. Using rolling cylinders, we experimentally produced diatom aggregates in the presence and absence of minerals and/or microzooplankton. Minerals and to a lesser extent microzooplankton decreased aggregate size and roughness and increased their sphericity and compactness. Stokes' Law parameterized with a fractal porosity modeled adequately size‐SV relationships for mineral‐loaded aggregates. Phytoplankton‐only aggregates and those exposed to microzooplankton followed the general Navier‐Stokes drag equation suggesting an indiscernible effect of microzooplankton and a drag coefficient too complex to be calculated with a Stokes' assumption. We compared our results with a larger data set of ballasted and nonballasted marine aggregates. This confirmed that the size‐SV relationships for ballasted aggregates can be simulated by Stokes' models with an adequate fractal porosity parameterization. Given the importance of mineral ballasting in the ocean, our findings could ease biogeochemical model parameterization for a significant pool of particles in the ocean and especially in the mesopelagic zone where the particulate organic matter : mineral ratio decreases. Our results also reinforce the importance of accounting for porosity as a decisive predictor of marine aggregate SV.

Biogenic sinking particle fluxes and sediment trap collection efficiency at Ocean Station Papa

“…9(1) page 7 of 24 regions were calculated using representative SVs of 100 and 500 m d -1 . Limited shipboard measurements of salp fecal pellets during EXPORTS showed SVs ranging hundreds of meters per day (D Steinberg, personal communication), similar to compilations of SV observations of sinking particles in the literature (e.g., Laurenceau-Cornec et al, 2019). Mean particle trajectories were computed from either the merged AVISO-ADCP velocity grid or the mean Revelle velocity time series.…”

Comment on bg-2020-481

“…The sinking speed of particles depends on their mineral composition (Le Moigne 2013), shape (Laurenceau et al, 2019) and on the phytoplankton community (Riley et al 2012, Guidi et al 2009. Consistent with our cytometric results, the pigment composition available at ST7, ST8 and ION show a community dominated by nanophytoplankton (>60% of total Chl-a) in the upper 80m, while diatoms were abundant at DCM depth (41-51% of total Chl-a, see Marañón et al 2020).…”

Influence of pycnocline on settling behaviour of non-spherical particle and wake evolution

“…Type 2 is represented by the settling behaviour of thick disks presented in detail in the results section ( Fig. 3) and has been observed in this study for Re ul ∈ (20,44) and Fr ul ∈ (1, 1.6). It is characterized by a tilted position in phase III, detachment of a wake and a bell-shaped structure on a jet, which is specific for this type and has not been observed for the other two types described herein.…”

“…It has been already demonstrated that standard formulas for particles settling in a homogeneous water column misestimate considerably the settling velocity and the residence time of spheres 24 and disks 39 , since they do not take into account the fact that density gradient in the column of fluid enhances drag acting on a particle. Moreover, researchers are more and more aware that oversimplifications of marine particles shape and density as well as the application of Stokes’ Law, which is dedicated to the settling of a sphere in the laminar Re number regime, may be the source of unreliable estimation of particulate flux in ocean models 44 , 45 . Better understanding of the dynamics of variously shaped particles settling in stratified systems is necessary to facilitate development of robust modelling approaches.…”