Collaborative Proposal: Form and function of phytoplankton in unsteady, low Reynolds-number flows

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Small-scale flow dynamics at low Reynolds numbers (Re) are important to phytoplankton cells in delivery of nutrients, sensory detection by and physical encounter with herbivores, accumulation of bacterial populations in the "phycosphere" or region immediately surrounding phytoplankton cells and coagulation of cells themselves as a mechanism terminating blooms. In nature most phytoplankton experience unsteady flows, i.e., velocities near the cells that vary with time due to the intermittency of turbulence and to discontinuous, spatially distributed pumping by herbivores. This unsteadiness has not previously been taken into account in models or measurements with plankton. Moreover, there have been decade- and century- long lags in moving relevant models of unsteady flow effects at low Re from applied mathematics and engineering to ecological applications. Engineering models show unsteady effects due to the history of formation of spatially extensive flow perturbations or wakes should be important to unsteady motions of moderately small biota. This project will address these affects. Non-swimming phytoplankton, and in particular diatoms, will be used as the simplest case where important unsteady flow behaviors should arise. This research activity will include a multi-level educational program, aimed at graduate research assistants, undergraduate research interns, undergraduate marine sciences majors and high-school teachers. Low-Re behaviors afford unusual opportunities to experience how mathematics, physics and biology inseparably catalyze understanding of phenomena that run counter to intuition. This activity will also include international collaborations with world experts on organism-flow interaction in Cambridge (T.J. Pedley) and Copenhagen (T. Kiorboe & A.W. Visser). The overall goals of the activity are to accelerate the flow of understanding from modelers to measurers to users of the information and back again. Educational materials that project U.S. national standards will be developed during intensive summer workshops with the high-school teachers and be made available on the web. Unsteady flow effects on phytoplankton will be predicted with explicit models based on singularity solutions (that involve the useful simplification that force is applied to the fluid at a small number of points) and mathematical models that include both the near field at low Re and the far field over a range of Re, both representative of nature. Singularity solutions allow explicit treatment of the role of complex cell shapes. Scaled-up analog models will be placed in a large Couette vessel to better visualize behaviors for both the research and teaching efforts. Natural-scale, but simplified, unsteady flows will be produced in smaller Couettes (nested, counter-rotating cylinders with seawater in the gap between the two cylinders) containing live phytoplankton and will be quantified by magnifying, particle-imaging velocimetry (PIV). Image analysis will be used to measure translation, rotation and flexural deformation of the phytoplankton. These studies will test various hypotheses derived from the general thesis that cell shapes and mechanical properties interact with unsteady flows to produce potentially fitness-enhancing, relative motions of the cell or chain and its surrounding fluids. A basic hypothesis is that unsteady fluid motion will interact with bending of cells to produce relative motion of fluid and phytoplankter. A very exciting prospect is that periodic instabilities known to arise at low Re may allow flexible organisms to act as "self-organizing engines" - through elasticity to harness energy from decaying turbulence and thereby move relative to the fluid. It is also expected that this study of passively bending structures in unsteady flows will help to understand the use of flexible appendages in swimming. The work is likely to aid significantly in associating functions with the shapes and spines of microplankton that are used in the identification of fossil specimens. By including relevant, unsteady fluid motions at low Re, the study will also provide firmer linkages between form and function in living plankton in the size range from 10 - 1000 mm that many large phytoplankton, invertebrate and fish larvae and other small zooplankton occupy.