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

低雷诺数（Re）下的小尺度流动动力学对于浮游植物细胞的营养物质输送、与食草动物的感官探测和物理接触、浮游植物细胞周围“藻圈”或区域内细菌种群的积累以及细胞本身的凝聚作为一种终止藻华的机制都是重要的。在自然界中，大多数浮游植物经历不稳定流动，即由于湍流的间歇性和食草动物的不连续、空间分布的泵送，细胞附近的速度随时间而变化。这种不稳定性以前在浮游生物的模型或测量中没有被考虑在内。此外，将低Re下非定常流动效应的相关模型从应用数学和工程应用到生态应用方面，已经有十年甚至一个世纪的滞后。工程模型表明，由于空间广泛的流动扰动或尾迹的形成历史而产生的非定常效应对于中等规模的生物群的非定常运动应该是重要的。这个项目将解决这些影响。非游动的浮游植物，特别是硅藻，将作为最简单的情况，其中重要的不稳定流动行为应该出现。这项研究活动将包括一个多层次的教育计划，针对研究生研究助理，本科生研究实习生，本科生海洋科学专业和高中教师。低re行为提供了不同寻常的机会来体验数学、物理和生物学是如何不可分割地催化对与直觉背道而驰的现象的理解的。这项活动还将包括与剑桥（T.J.佩德利）和哥本哈根（T.J. Kiorboe &amp； A.W. Visser）的世界专家就生物流动相互作用进行国际合作。该活动的总体目标是加速从建模者到度量者再到信息用户的理解流，然后再返回。反映美国国家标准的教育材料将在与高中教师的密集夏季研讨会上开发，并在网上提供。非定常流对浮游植物的影响将用基于奇异解的显式模型来预测（这涉及到在少数点上对流体施加力的有用简化）和数学模型，其中包括低Re的近场和Re范围内的远场，两者都代表了自然。奇点解允许明确处理复杂细胞形状的作用。放大的模拟模型将被放置在一个大型的Couette容器中，以便更好地可视化研究和教学工作的行为。自然尺度的、简化的非定常流动将在含有活浮游植物的较小的couette（嵌套的、反向旋转的圆柱体，两个圆柱体之间的间隙有海水）中产生，并将通过放大粒子成像测速仪（PIV）进行量化。图像分析将用于测量浮游植物的平移、旋转和弯曲变形。这些研究将测试各种假设，这些假设来源于一般的理论，即细胞形状和机械特性与非定常流相互作用，从而产生潜在的增强健康的细胞或链及其周围流体的相对运动。一个基本的假设是，不稳定的流体运动将与细胞的弯曲相互作用，产生流体和浮游植物的相对运动。一个非常令人兴奋的前景是，已知在低Re下出现的周期性不稳定性可能允许柔性生物体充当“自组织引擎”——通过弹性利用衰变湍流中的能量，从而相对于流体移动。对非定常流场被动弯曲结构的研究也将有助于理解柔性附属物在游泳中的应用。这项工作很可能有助于将功能与用于鉴定化石标本的微型浮游生物的形状和刺联系起来。通过纳入相关的、低Re下的非定常流体运动，该研究还将在10 - 1000毫米的浮游生物中提供更牢固的形式和功能之间的联系，许多大型浮游植物、无脊椎动物和鱼类幼虫以及其他小型浮游动物占据着这些浮游生物。

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.