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

在低雷诺数（Re）的小规模流动动力学是重要的浮游植物细胞在输送营养物质，感官检测和物理接触食草动物，积累的细菌种群的“藻圈”或区域直接周围的浮游植物细胞和细胞本身的凝结作为一种机制终止水华。在自然界中，大多数浮游植物经历不稳定的流动，即，由于湍流的不连续性和食草动物的不连续的、空间分布的泵送，细胞附近的速度随时间变化。这种不稳定性以前没有被考虑在模型或测量浮游生物。 此外，在将低Re下的非定常流效应的相关模型从应用数学和工程学转移到生态学应用方面，已经滞后了十年和世纪之久。 工程模型表明，由于空间上广泛的流动扰动或尾迹的形成历史，对中等规模生物群的非定常运动应该是重要的。 本项目将解决这些影响。 非游泳浮游植物，特别是硅藻，将被用作最简单的情况下，重要的非定常流行为应该出现。 这项研究活动将包括一个多层次的教育方案，针对研究生研究助理，本科研究实习生，本科海洋科学专业和高中教师。低Re行为提供了不寻常的机会，体验数学，物理学和生物学如何不可分割地催化对与直觉背道而驰的现象的理解。 这项活动还将包括与世界各地的生物体-流相互作用专家在剑桥（T. J. Pedley）和哥本哈根（T. Kiorboe A.W. Visser）。 这项活动的总体目标是加速从建模者到测量者再到信息用户的理解流动。将在与高中教师的暑期密集讲习班期间编写反映美国国家标准的教育材料，并在网上提供。非定常流对浮游植物的影响将通过基于奇点解的显式模型（涉及在少量点处对流体施加力的有用简化）和包括低Re下的近场和Re范围内的远场的数学模型进行预测，两者都代表自然界。奇异性解决方案允许明确处理复杂细胞形状的作用。按比例放大的模拟模型将被放置在一个大型库埃特容器，以更好地可视化行为的研究和教学工作。将在含有活浮游植物的较小Couettes（嵌套、反向旋转的圆柱体，两个圆柱体之间的差距中有海水）中产生自然尺度但简化的非定常流，并将通过放大、粒子成像测速仪（PIV）进行量化。图像分析将被用来测量浮游植物的平移，旋转和弯曲变形。 这些研究将测试来自一般论文的各种假设，即细胞形状和机械性能与不稳定流动相互作用，产生潜在的健身增强，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，产生流体和植物生长因子的相对运动。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”--通过弹性利用来自衰减湍流的能量，从而相对于流体运动。也可以预期，被动弯曲结构在非定常流中的研究将有助于理解在游泳中使用的柔性附件。这项工作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。通过纳入低Re下的相关非稳定流体运动，该研究还将提供10 - 1000毫米大小的活浮游生物的形式和功能之间更牢固的联系，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.