Theoretical hydrodynamic efficiency of coccoliths

Abstract

Abstract The sinking speed of coccoliths, considered as small particles, mainly depends on turbulence processes in the upper layer of the ocean. In deeper layers, the size, shape, buoyancy, and drag force experienced between the contact surface and the fluid in which particles are immersed are fundamental determinants of the sinking speed. For spherical bodies, the sinking speed is explained by the Stokes formula. For other geometries, it can be explained by the shape resistance factor of an equivalent sphere with the same density and volume as the original body. To model the sinking trajectories of coccoliths in the upper layer, a Lagrangian turbulence model was applied. To estimate how the size and shape of some coccoliths influence their sinking speed and trajectory in deeper layers, experimental videos were taken of sinking coccoliths made at amplified scales in a graduated water tank and analyzed. In the upper layer, the sinking speed only depends on the intensity of turbulence. Below this layer, the shape resistance factor reduced the sinking speed with respect to that of the equivalent sphere by an average of 50%. The Lagrangian model shows that, in the turbulent mixing layer, the distribution of particles is homogeneous, but once the particles fall below the laminar layer, the distribution takes on the form of a thin lens with a central thickness that is proportional to the sinking speed. The particles then flatten out to a thin strip as they continue along their path to the ocean bottom.