SIAM News Blog

Fluid Mechanics of Plankton

By Karthika Swamy Cohen and Lina Sorg

Large concentrations of plankton are found in oceans and other water bodies, often many miles long and a few feet thick. They make up the base of many aquatic food webs, and are frequently subject to varying levels of turbulence. Yet researchers have only recently begun using quantitative models to represent turbulence’s impact on the behavior and physiology of planktonic cells.  

In the last few decades, math modeling has been instrumental in understanding organism motility. The same can be said of plankton, which direct their motility via chemotaxis, the ability to sense chemical radiance and adjust movement accordingly. Researchers use mathematical frameworks that model chemotaxis and yield important information about diffusion, consumption, and turbulent movement. 

In an invited talk at the SIAM Annual Meeting entitled “The Turbulent Life of Plankton,” Roman Stocker (ETH Zürich) described quantitative models to demonstrate turbulence’s unexpected effects on plankton. 

Stocker focuses his work on motile phytoplankton cells. 90% of the phytoplankton that produce red tides—large, sometimes-harmful algal blooms that can contaminate fisheries and cause illness in both humans and animals—are motile.  

An oscillating signal indicates that phytoplankton swim to surface in morning and down at night in a vertical migration.  In still waters, their movement remains vertical and straight. Ocean currents, however, can create shear forces that occur between layers of water. These forces act on plankton, causing them to change their direction from vertical to inclined. When forces are strong enough they can also cause plankton to tumble and spin.

“It’s like walking with a strong wind at your back, which makes you lean forward, and when it blows very hard, it can knock you down,” said Stocker, explaining the way the forces work.

Interaction between motile phytoplankton and fluid shear can drive thin phytoplankton layers. Very often these phytoplankton layers are shown to bloom not just at the surface but also in depths many meters beneath the ocean surface. Such activity can be a precursor for harmful red tides, and has potential implications for the ecosystem. 

Using millifluidic experiments—powerful microfabrication techniques—and mathematical modeling, Stocker and his team have shown that plankton motility can explain these thin layers of high phytoplankton concentration. Simulations and optimal foraging theory model the fate of organic matter during aquatic turbulence. 

“Motile phytoplankton tend to dislike turbulence,” Stocker said and went on to explain how the phenomenon known as Margalef’s mandala causes turbulence, disrupting the equilibrium regime and hindering plankton’s ability to make the vertical swim to the surface necessary for photosynthesis. Additionally, viscous torque makes microorganisms tumble, similar to how the wind blows a soccer ball around on a windy day. 

Thus, the following question dominates Stocker’s lab work: can phytoplankton actively respond to turbulence? To answer this question, Stocker’s group created a flip chamber, which mimics cell overturning by turbulence. 

In the ocean, phytoplankton experience vorticity; rather than a vortex or two, they experience a periodicity of vortices. In order to simulate this accurately, Stocker’s group uses an automated experiment with multiple flips in 30 seconds. In the absence of flipping, plankton are seen to display gravitaxis and swim vertically. When they are subject to flipping again, they appear to return to exactly the same distribution.

As a result of the turbulence, some cells—which have control over their surface shape—completely change behavior. Flipping the plankton in a vertical rather than a horizontal plane makes the distribution much more symmetric. 

“Phytoplankton know a lot more fluid mechanics than we give them credit for,” said Stocker in conclusion.  Understanding the turbulence to which plankton is subjected will allow further modeling opportunities for researchers to better understand their role in various ecosystems. “I hope I’ve convinced you that there are many areas in this domain that benefit from mathematical modeling,” he said. 

Karthika Swamy Cohen is the managing editor of SIAM News.
Lina Sorg is the associate editor ofSIAM News.
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