Microscale Patches of Nonmotile Phytoplankton

Phytoplankton cells have evolved sophisticated strategies for actively responding to environmental signals, most notably to mechanical stresses of hydrodynamic origin. A largely unanswered question, however, is the significance of these cellular responses for the largely heterogeneous spatial distribution of cells found in the oceans. Motivated by the physiological regulation of buoyancy prevalent in nonmotile phytoplankton species, we solve here a minimal model for “active” sinking that incorporates these cellular responses. Within this model, we show how buoyancy regulation leads to intense patchiness for nonmotile species as compared to passive tracers, resulting in important variations in settling speeds and, as a consequence, determining escape rates to the deep ocean.

Figure 1

Representative trajectories for $R=0.4$, $\mathrm{St}=0.1$, $\alpha =0.1$, and $v_s=0.15$ (a), $v_s=0.325$ (b), $v_s=0.475$ (c), and $v_s=0.525$ (d). In all panels and subsequent figures, the green lines (light grey) correspond to the passive case, the shear-thinning case is depicted in blue (dark grey), and the shear-thickening case is depicted in red (medium grey). All trajectories were initialized at the same (or equivalent in the doubly periodic domain) initial position (marked as a white circle) while the final steady state is marked in black. Background gray scale and arrows correspond respectively to the vorticity and velocity field of the Taylor-Green vortex flow.

Figure 2

The area of attraction (a) and the averaged sedimentation velocity of particles departing out of the area of attraction (b) for passive (light grey), shear-thinning (dark grey), and shear-thickening (intermediate grey) buoyancy control as function of the still fluid sedimentation velocity, $v_s$. The 45° dashed line in panel (b) is a visual guide for $⟨v_z⟩=v_s$.

Figure 3

The probability distribution of $\tau$ for (a) passive particles and (b) the shear-thickening case, with $v_s=0.305$ and $n=10$. (c) Contour plots of the spatial distribution of $\tau$ for the same parameter set. Trajectories plotted in black correspond with the four attractive limit cycles that emerge for $v_s\gtrsim 0.3$. Dashed (flat) filled bars in (b) correspond respectively to the distribution within (outside) the area enclosed by the black limit cycles shown in (c).

Figure 4

(a) The accumulation index $\mathrm{\Psi }$ of permanently suspended particles as a function of particle radius $a$ for passive (green line), shear-thinning (blue line), and shear-thickening (red line) buoyancy control. The different curves correspond to different scales within the Kolmogorov range as highlighted with squares in panel (b). The shaded area in (b) marks the typical range of values for the ocean.