Low-Reynolds-number swimming at pycnoclines

Abstract

Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the "squirmer." We identify the Richardson number-the ratio of buoyancy forces to viscous forces-as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes.stratified fluid | bio-locomotion V ertical variations in water density, or "pycnoclines," occur ubiquitously in aquatic and marine environments (1), due to gradients in temperature (thermoclines) or salinity (haloclines). Pycnoclines can trigger a wide range of environmental and oceanographic processes. In oceans and lakes, intense biological activity and accumulation of organisms and particles are associated with pycnoclines (2, 3). For example, formation of phytoplankton blooms is often correlated with stratification (3), and these blooms can enhance CO 2 sequestration (4) or disrupt water supply systems (5). Stratification can also affect organism migration: Some species of euphausiids do not cross thermoclines (6) and haloclines can act as a barrier to the vertical migration of dinoflagellates (7).Despite the widespread ecological implications of stratification, its hydrodynamic effects on organisms remain poorly understood. This is partly due to the notion that most organisms are too small to be affected by stratification, because the water density varies on a length scale, L ρ ¼ ρ 0 ∕γ ∼ OðkmÞ, much larger than the size of the organism, where ρ 0 is a reference density (e.g., 1;000 kg m −3 ) and γ is the vertical gradient in water density [typical values of γ range from Oð0.01Þ kg m −4 at ocean thermocline (8) to Oð1Þ kg m −4 in fjords and lakes (2, 3)].This notion is incorrect. It was recently found that the appropriate length scale to determine whether stratification affects motion is L ¼ ðμκ∕γgÞ 1∕4 , where μ is the dynamic viscosity, κ the diffusivity of the stratifying agent, and g the acceleration of gravity (9). [This length scale was earlier derived, in a different context, by List (10)]. Organisms larger than L are affected by stratification. For typical stratifications, L is in...

Active suspensions in thin films: nutrient uptake and swimmer motion

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Formation and maintenance of high-nitrate, low pH layers in the eastern Indian Ocean and the role of nitrogen fixation

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