CAS: Estimates of the decay of diffusion induced flows in strongly stratified fluids and ergodic mixing properties of solutes driven by randomly moving walls in viscous fluids.

海洋在吸收和隔离地球大气层中的碳方面发挥着核心作用。 因此，了解这一过程如何运作对于预测地球气候的未来演变至关重要。 其基本机制是，大气中溶解的二氧化碳气体被浮游植物通过光合作用转化为固体碳，然后沉入海底，最终在海底变成石油。 这种固体下沉碳是如何形成大颗粒团簇的，目前还没有很好的理解，这是该奖项的重点。 PI最近通过实验发现并从理论上解释了分层沃茨中粒子团簇形成的一种新机制，该机制仅依赖于密度分层和引力的存在。 他们证实，悬浮在分层沃茨中的颗粒可以产生它们自己的流体流动，从而吸引附近的其他颗粒形成更大的团簇聚集体。 这一现象提供了一种可能的机制，解释了所谓的海洋雪是如何在海洋沃茨中形成的。 了解颗粒聚集体形成的细节对于预测海洋吸收碳的数量和速度是必要的，该奖项旨在提高我们对这一基本过程的理解。该项目还为研究生提供研究培训机会。最近发现的PI，涉及自组装在分层流体和遍历行为的扩散溶质平流随机剪切层，已经确定了许多新的基本问题的基本机制负责这些现象。对于自组装的情况下，单个和多个机构的扩散诱导流将进行研究分析，计算，和实验的目标是开发一个统一有效的渐近展开在低和高Peclet数。这将包括对PI实验观察到的耦合球体有限时间坍塌的机制和作用力进行深入研究。我们的工作是理解大规模聚集体如何在分层沃茨中形成的第一步。 在遍历性的背景下，使用中心流形技术的新的渐近理论将被应用到非平面壁随机移动的粘性流体。 我们探讨如何随机性，通过壁面运动注入，传播到流体和溶解的溶质，以更好地了解物理上可实现的非剪切流的混合。 通过扩散诱导流动对混合和自组装的研究有望提高我们对海洋聚集体形成的认识，最终确定海洋中碳沉降的时间尺度。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The oceans play a central role in absorbing and sequestering carbon from the Earth's atmosphere. As such, understanding how this process works is crucial to predicting the future evolution of the planet's climate. The basic mechanism is one in which dissolved carbon-dioxide gas from the atmosphere is converted by phytoplankton, through photosynthesis, into solid carbon, which then sinks to the ocean bottom, where it is eventually turned into oil over the eons. Precisely how this solid sinking carbon forms into large particle clusters is not well understood, and it is a focus of this award. The PIs have recently experimentally discovered and theoretically explained a novel mechanism for the creation of particle clusters in stratified waters which only relies upon the presence of density stratification and gravitation. They established that particles suspended in stratified waters can create their own fluid flows, which draw other nearby particles into forming larger cluster aggregations. This phenomenon offers a possible mechanism for how the so-called Marine Snow, agglomerates of sedimenting carbon-rich "flakes," may form in ocean waters. Understanding the details of particle aggregate formation is necessary for predicting how much and how fast the ocean can absorb carbon, and this award seeks to improve our understanding of this fundamental process. The project also provides research training opportunities for graduate students. Recent discoveries by the PIs, involving self-assembly in stratified fluids and ergodic behavior of diffusing solutes advected by random shear layers, have identified many new fundamental questions regarding the underlying mechanisms responsible for these phenomena. For the case of self-assembly, diffusion-induced flows for single and multiple bodies will be studied analytically, computationally, and experimentally with the goal of developing a uniformly valid asymptotic expansion at both low and high Peclet numbers. This will include an in-depth study of the mechanisms and forces at play for the finite time collapse of coupled spheres experimentally observed by the PIs. Our work is the first step in understanding how large-scale aggregates may form in stratified waters. In the context of the ergodicity, new asymptotic theories using center manifold techniques will be applied to non-flat walls randomly moving in viscous fluids. We explore how randomness, injected through the wall motion, propagates into the fluid and into dissolved solutes to better understand mixing in physically realizable non-sheared flows. The study of both mixing and self-assembly by diffusion-induced flows is expected to improve our knowledge of ocean aggregate formation, which ultimately sets the timescales for carbon sinking in the ocean.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.