Preferential concentration of noninertial buoyant particles in the ocean mixed layer under free convection

In this work we investigate buoyant particle dynamics in the ocean mixed layer (OML) under a purely convective regime. We focus on noninertial particles that are lighter than the surrounding seawater (thus, buoyant), which is a useful configuration when representing oil, microplastic debris, and other buoyant materials that do not necessarily exhibit strong inertial effects. Our main goal is to understand and describe the physical mechanisms that control the buoyant particles' surface concentration under such conditions, specifically the preferential concentration effects that arise independently of inertia (rather than the well-known centrifuging mechanism for heavy particles). In our investigation we use large-eddy simulation to model the particle dispersion in the OML in which the evolution of the particle field is simulated using an Eulerian approach. We find that in addition to the preferential concentration effect that clusters particles into convergence regions on the surface (which is a well-known and straightforward effect on free surfaces), there is a secondary effect for highly buoyant particles that drives them into vorticity-dominated regions. We explain this effect as the advection of buoyant particles by persistent vortices in the flow, which turns out to be the dominating mechanism controlling the surface particle distribution. Highly buoyant particles are trapped in the interior of the vortices (at the surface), which favors clustering in vorticity-dominated regions, while for particles with low buoyancy this effect is negligible.

Figure 1

Normalized surface concentrations for particles (a) C0.19, (b) C0.44, and (c) C1.21 (in order of increasing buoyancy) and (d) horizontal divergence $D$ at the surface. Here $h$ is the OML depth and all panels correspond to the same instant in time; $C_{*}$ is a concentration scale, whose details will be given in Sec. 3.

Figure 2

Joint probability density function of the horizontal divergence $D$ [see Eq. (2)] and the Okubo parameter $Q$ [see Eq. (9)] for the flow field at the surface. The labels in each of the quadrants defined by the red lines are the flow classifications according to Okubo [32].

Figure 3

Detail of (a) a strong vertical vortex and (b) several vertical vortices in a small region of the simulation domain. The color contours shown at the top surface are the 2D Okubo parameter $Q$ and the isosurface is a surface of constant 3D Okubo-Weiss parameter $Q_{3\text{D}}$.

Figure 4

Time evolution of normalized $P$-conditioned average particle concentration $C_P(P,t_{*})$ for C0.00, C0.19, C0.44, C0.59, C0.78, and C3.11. Here ${\langle C\rangle }_s$ is the average particle concentration at the surface. Data are smoothed by averaging over logarithmically spaced bins.

Figure 5

Steady state for $P$-conditioned surface concentrations (normalized by average surface concentration) for different types of surface flow structures and different particle cases (plotted as $\beta$).

Figure 6

Concentration map of the conditioned average surface concentration ${\langle C|(Q,D)\rangle }_s$ normalized by surface concentration for particles C0.00, C0.19, C0.44, and C0.05 in steady state.

Figure 7

Sequence of snapshots at increasing time (from top to bottom) of the Okubo parameter $Q$, particle mass concentration $C$, and vorticity on the surface. Each set of panels, from (a) to (d), is a different time, which is indicated on the right of the figure. The sequence shows a constructive interaction and the colormaps are the same as in Fig. 1.

Figure 8

Sequence of snapshots at increasing time (from top to bottom) of the Okubo parameter $Q$, particle mass concentration $C$, and vorticity on the surface. Each set of panels, from (a) to (d), is a different time, which is indicated on the right of the figure. The sequence illustrates a destructive vortex interaction and the colormaps are the same as in Fig. 1.

Figure 9

Profiles of (a) $u_{\alpha }$ ($u, v$, and $w$) variances, (b) vertical velocity skewness, and (c) heat flux for steady state.