Submesoscale coupling of krill and whales revealed by aggregative Lagrangian coherent structures.

In the marine environment, dynamic physical processes shape biological productivity and predator-prey interactions across multiple scales. Identifying pathways of physical-biological coupling is fundamental to understand the functioning of marine ecosystems yet it is challenging because the interactions are difficult to measure. We examined submesoscale (less than 100 km) surface current features using remote sensing techniques alongside ship-based surveys of krill and baleen whale distributions in the California Current System. We found that aggregative surface current features, represented by Lagrangian coherent structures (LCS) integrated over temporal scales between 2 and 10 days, were associated with increased (a) krill density (up to 2.6 times more dense), (b) baleen whale presence (up to 8.3 times more likely) and (c) subsurface seawater density (at depths up to 10 m). The link between physical oceanography, krill density and krill-predator distributions suggests that LCS are important features that drive the flux of energy and nutrients across trophic levels. Our results may help inform dynamic management strategies aimed at reducing large whales ship strikes and help assess the potential impacts of environmental change on this critical ecosystem.

Topological analysis of particle transport in lung airways: Predicting particle source and destination.

Particle transport in lung airways can induce respiratory disease and play a vital role in aerosol drug delivery. Herein, we present dynamical systems features that influence airflow and particle transport in the tracheobronchial trees. Computational fluid dynamics (CFD) was used to solve for unsteady airflow in a patient-specific model. Particle tracking simulations were performed for micron-size particles. The destination map that connects the particle final location to the initial location and injection time was constructed. Finite-time Lyapunov exponent (FTLE) fields were calculated to identify inertial Lagrangian coherent structures (ILCS), topological features that act as separatrices. Our results demonstrated that these topological features control the destination map at the trachea. The temporal evolution of ILCS influenced the sensitivity of particle transport fate to injection time, whereas the emergence of new ILCS with an increased integration time controlled transport to different generations of airways. Additionally, particles starting at the ILCS were shown to mostly deposit at the airway walls. Finally, an innovative source inversion strategy was introduced to integrate the Maxey-Riley equation backward in time and identify the origin of dispersed particles. Our study explores novel dynamical systems tools that improve our understanding of particle transport and deposition in the airways and could be used to guide future targeted drug delivery studies.

Flow stagnation volume and abdominal aortic aneurysm growth: Insights from patient-specific computational flow dynamics of Lagrangian-coherent structures.

Abdominal aortic aneurysms (AAA) are localized, commonly-occurring dilations of the aorta. When equilibrium between blood pressure (loading) and wall mechanical resistance is lost, rupture ensues, and patient death follows, if not treated immediately. Experimental and numerical analyses of flow patterns in arteries show direct correlations between wall shear stress and wall mechano-adaptation with the development of zones prone to thrombus formation. For further insights into AAA flow topology/growth interaction, a workout of patient-specific computational flow dynamics (CFD) is proposed to compute finite-time Lyapunov exponents and extract Lagrangian-coherent structures (LCS). This computational model was first compared with 4-D phase-contrast magnetic resonance imaging (MRI) in 5 patients. To better understand the impact of flow topology and transport on AAA growth, hyperbolic, repelling LCS were computed in 1 patient during 8-year follow-up, including 9 volumetric morphologic AAA measures by computed tomography-angiography (CTA). LCS defined barriers to Lagrangian jet cores entering AAA. Domains enclosed between LCS and the aortic wall were considered to be stagnation zones. Their evolution was studied during AAA growth. Good correlation - 2-D cross-correlation coefficients of 0.65, 0.86 and 0.082 (min, max, SD) - was obtained between numerical simulations and 4-D MRI acquisitions in 6 specific cross-sections from 4 patients. In follow-up study, LCS divided AAA lumens into 3 dynamically-isolated zones: 2 stagnation volumes lying in dilated portions of the AAA, and circulating volume connecting the inlet to the outlet. The volume of each zone was tracked over time. Although circulating volume remained unchanged during 8-year follow-up, the AAA lumen and main stagnation zones grew significantly (8 cm3/year and 6 cm3/year, respectively). This study reveals that transient transport topology can be quantified in patient-specific AAA during disease progression by CTA, in parallel with lumen morphology. It is anticipated that analysis of the main AAA stagnation zones by patient-specific CFD on a yearly basis could help to predict AAA growth and rupture.

Chaotic Manifold Analysis of Four-Screw Extruders Based on Lagrangian Coherent Structures.

The four-screw extruder (FSE) is a novel equipment for polymer processing. In this paper, from a new viewpoint of Lagrangian coherent structures (LCS), two-dimensional fluid transport and chaotic mixing characteristics within three kinds of novel industrial FSEs are explored based on LCS to better understand the flow and mixing natures in the FSEs. Firstly, based on the finite-time invariant manifold theory, the finite-time Lyapunov exponent (FTLE) and LCS of FSEs are calculated by considering the different initial time. Hyperbolic LCSs from the FTLE maps are adopted to identify chaotic mixing manifolds in FSEs. Moreover, particle tracking and Poincaré sections are used to illustrate the different fluid motions in the above three isolated regions. Finally, the effects of relative rotating directions and layout of four screws on the chaotic manifolds in FESs are discussed in order to enhance local mixing performance. Furthermore, quantitative mixing measures, such as the segregation scale, logarithmic of stretching, and mean-time mixing efficiency are employed to compare the mixing efficiencies in three kinds of FSEs. The results show that the relative rotating directions and positions of four screws can change the chaotic manifolds and increase mixing performance in local poor mixing regions. FTLE and LCS analysis are helpful to better understand the chaotic mixing nature in the novel screw extruders.