Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

Teamwork in the viscous oceanic microscale

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kanso, E. A., Lopes, R. M., Strickler, J. R., Dabiri, J. O., & Costello, J. H. Teamwork in the viscous oceanic microscale. Proceedings of the National Academy of Sciences of the United States of America, 118(29), (2021): e2018193118, https://doi.org/10.1073/pnas.2018193118.Nutrient acquisition is crucial for oceanic microbes, and competitive solutions to solve this challenge have evolved among a range of unicellular protists. However, solitary solutions are not the only approach found in natural populations. A diverse array of oceanic protists form temporary or even long-lasting attachments to other protists and marine aggregates. Do these planktonic consortia provide benefits to their members? Here, we use empirical and modeling approaches to evaluate whether the relationship between a large centric diatom, Coscinodiscus wailesii, and a ciliate epibiont, Pseudovorticella coscinodisci, provides nutrient flux benefits to the host diatom. We find that fluid flows generated by ciliary beating can increase nutrient flux to a diatom cell surface four to 10 times that of a still cell without ciliate epibionts. This cosmopolitan species of diatom does not form consortia in all environments but frequently joins such consortia in nutrient-depleted waters. Our results demonstrate that symbiotic consortia provide a cooperative alternative of comparable or greater magnitude to sinking for enhancement of nutrient acquisition in challenging environments.We are grateful to Y. Garcia for help with organism sampling and sorting. E.A.K. is funded by NSF-2100209, NSF RAISE IOS-2034043 and NIH R01 HL 153622-01A1. R.M.L. is a CNPq research fellow (grant # 310642/2017-5). J.H.C. and J.O.D. are funded by Grant NSF-2100705

Motile cilia create fluid-mechanical microhabitats for the active recruitment of the host microbiome

We show that mucociliary membranes of animal epithelia can create fluid-mechanical microenvironments for the active recruitment of the specific microbiome of the host. In terrestrial vertebrates, these tissues are typically colonized by complex consortia and are inaccessible to observation. Such tissues can be directly examined in aquatic animals, providing valuable opportunities for the analysis of mucociliary activity in relation to bacteria recruitment. Using the squid–vibrio model system, we provide a characterization of the initial engagement of microbial symbionts along ciliated tissues. Specifically, we developed an empirical and theoretical framework to conduct a census of ciliated cell types, create structural maps, and resolve the spatiotemporal flow dynamics. Our multiscale analyses revealed two distinct, highly organized populations of cilia on the host tissues. An array of long cilia (∼25 μm) with metachronal beat creates a flow that focuses bacteria-sized particles, at the exclusion of larger particles, into sheltered zones; there, a field of randomly beating short cilia (∼10 μm) mixes the local fluid environment, which contains host biochemical signals known to prime symbionts for colonization. This cilia-mediated process represents a previously unrecognized mechanism for symbiont recruitment. Each mucociliary surface that recruits a microbiome such as the case described here is likely to have system-specific features. However, all mucociliary surfaces are subject to the same physical and biological constraints that are imposed by the fluid environment and the evolutionary conserved structure of cilia. As such, our study promises to provide insight into universal mechanisms that drive the recruitment of symbiotic partners

A fundamental propulsive mechanism employed by swimmers and flyers throughout the animal kingdom

Even casual observations of a crow in flight or a shark swimming demonstrate that animal propulsive structures bend in patterned sequences during movement. Detailed engineering studies using controlled models in combination with analysis of flows left in the wakes of moving animals or objects have largely confirmed that flexibility can confer speed and efficiency advantages. These studies have generally focused on the material properties of propulsive structures (propulsors). However, recent developments provide a different perspective on the operation of nature\u27s flexible propulsors, which we consider in this Commentary. First, we discuss how comparative animal mechanics have demonstrated that natural propulsors constructed with very different material properties bend with remarkably similar kinematic patterns. This suggests that ordering principles beyond basic material properties govern natural propulsor bending. Second, we consider advances in hydrodynamic measurements demonstrating suction forces that dramatically enhance overall thrust produced by natural bending patterns. This is a previously unrecognized source of thrust production at bending surfaces that may dominate total thrust production. Together, these advances provide a new mechanistic perspective on bending by animal propulsors operating in fluids - either water or air. This shift in perspective offers new opportunities for understanding animal motion as well as new avenues for investigation into engineered designs of vehicles operating in fluids