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中的碳方面发挥着核心作用。因此，了解这一过程是如何运作的，对于预测地球气候的未来演变至关重要。其基本机制是，浮游植物通过光合作用将大气中溶解的二氧化碳气体转化为固体碳，固体碳然后沉入海底，在那里最终转化为石油。这种固体下沉的碳是如何形成大颗粒簇的，目前还不清楚，这是这个奖项的一个焦点。PI最近在实验上发现并从理论上解释了分层水域中颗粒团形成的一种新机制，这种机制仅依赖于密度层化和重力的存在。他们证实，悬浮在分层水域中的颗粒可以产生自己的流体，从而吸引附近的其他颗粒形成更大的星团聚集体。这一现象为海洋积雪提供了一种可能的机制，海洋积雪是由沉积的富含碳的“薄片”凝聚而成的，它可能会在海水中形成。了解颗粒聚集体形成的细节对于预测海洋可以吸收多少碳以及吸收多快是必要的，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了研究培训机会。PI的最新发现，包括分层流体中的自组装和随机剪切层平流的扩散溶质的遍历行为，发现了许多关于导致这些现象的潜在机制的新的基本问题。对于自组装的情况，将通过解析、计算和实验研究单体和多体的扩散诱导流动，目标是在低Peclet数和高Peclet数下建立一致有效的渐近展开式。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。我们的工作是了解分层水域中如何形成大规模聚集体的第一步。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于在粘性流体中随机运动的非平坦壁面。我们探索了通过壁面运动注入的随机性如何传播到流体和溶解的溶质中，以更好地理解物理上可实现的非剪切流动中的混合。扩散诱导流动的混合和自组装研究有望提高我们对海洋聚集体形成的知识，这最终设定了碳在海洋中下沉的时间尺度。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.