Abstract
Negatively buoyant phytoplankton play an important role in the sequestration of CO_2 from the atmo-sphere and are fundamental to the health of the world’s fisheries. However, there is still much to discoveron transport mechanisms from the upper photosynthetic regions to the deep ocean. In contrast to intuitive
expectations that mixing increases plankton residence time in light-rich regions, recent experimental and computational evidence suggests that turbulence can actually enhance sedimentation of negatively buoyant diatoms. Motivated by these studies we dissect the enhanced sedimentation mechanisms using the simplest possible two-dimensional flows, avoiding expensive computations and obfuscation. In particular, we find that in vertical shear, preferential flow alignment and aggregation in down-welling regions both increase sedimentation, whereas horizontal shear reduces the sedimentation due only to alignment. However the magnitude of the shear does not affect the sedimentation rate. In simple vertical
Kolmogorov flow elongated particles also have an enhanced sedimentation speed as they spend more time in down-welling regions of the flow with vertically aligned orientation, an effect that increases with the magnitude of shear. An additional feature is identified in horizontal Kolomogorov flow, whereby the
impact of shear-dependent sedimentation speed is to cause aggregation in regions of high-shear where the sedimentation speed is minimum. In cellular flow, there is an increase in mean sedimentation speed with aspect ratio and shear strength associated with aggregation in down-welling regions. Furthermore,
spatially projected trajectories can intersect and give rise to chaotic dynamics, which is associated with a depletion of particles within so called retention zones.
expectations that mixing increases plankton residence time in light-rich regions, recent experimental and computational evidence suggests that turbulence can actually enhance sedimentation of negatively buoyant diatoms. Motivated by these studies we dissect the enhanced sedimentation mechanisms using the simplest possible two-dimensional flows, avoiding expensive computations and obfuscation. In particular, we find that in vertical shear, preferential flow alignment and aggregation in down-welling regions both increase sedimentation, whereas horizontal shear reduces the sedimentation due only to alignment. However the magnitude of the shear does not affect the sedimentation rate. In simple vertical
Kolmogorov flow elongated particles also have an enhanced sedimentation speed as they spend more time in down-welling regions of the flow with vertically aligned orientation, an effect that increases with the magnitude of shear. An additional feature is identified in horizontal Kolomogorov flow, whereby the
impact of shear-dependent sedimentation speed is to cause aggregation in regions of high-shear where the sedimentation speed is minimum. In cellular flow, there is an increase in mean sedimentation speed with aspect ratio and shear strength associated with aggregation in down-welling regions. Furthermore,
spatially projected trajectories can intersect and give rise to chaotic dynamics, which is associated with a depletion of particles within so called retention zones.
| Original language | English |
|---|---|
| Pages (from-to) | 743-766 |
| Journal | IMA Journal of Applied Mathematics |
| Volume | 83 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 25 Jul 2018 |
Bibliographical note
© The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for detailsKeywords
- plankton, diatoms, enhanced sedimentation, aspect ratio, shear flow, buoyancy
