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.

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

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.