Reconfiguration and the reduction of vortex-induced vibrations in broad leaves

Influence of the vessel wall geometry on the wall-induced migration of red blood cells

The geometry of the blood vessel wall plays a regulatory role on the motion of red blood cells (RBCs). The overall topography of the vessel wall depends on many features, among which the endothelial lining of the endothelial surface layer (ESL) is an important one. The endothelial lining of vessel walls presents a large surface area for exchanging materials between blood and tissues. The ESL plays a critical role in regulating vascular permeability, hindering leukocyte adhesion as well as inhibiting coagulation during inflammation. Changes in the ESL structure are believed to cause vascular hyperpermeability and entrap immune cells during sepsis, which could significantly alter the vessel wall geometry and disturb interactions between RBCs and the vessel wall, including the wall-induced migration of RBCs and the thickening of a cell-free layer. To investigate the influence of the vessel wall geometry particularly changed by the ESL under various pathological conditions, such as sepsis, on the motion of RBCs, we developed two models to represent the ESL using the immersed boundary method in two dimensions. In particular, we used simulations to study how the lift force and drag force on a RBC near the vessel wall vary with different wall thickness, spatial variation, and permeability associated with changes in the vessel wall geometry. We find that the spatial variation of the wall has a significant effect on the wall-induced migration of the RBC for a high permeability, and that the wall-induced migration is significantly inhibited as the vessel diameter is increased.

Measurement of morphological changes of pear leaves in airflow based on high-speed photography

The morphological changes of leaves under the airflow have a significant effect on the deposition of pesticide droplets on the leaves, but the wind-induced vibration of the leaves is complicated to measure. In this study, an aerodynamic test of the pear leaf was conducted in the wind tunnel, and binocular high-speed photography was used to record the deformation and vibration of the leaves under various airflow velocities. Experiments showed that air velocity (v) had a significant effect on the morphological response of the leaf. As v increased, the leaf was in three states, including static deformation, low-frequency vibration, and reconfiguration of airfoil steady state. The mutation from one state to another occurred at the critical velocity of v_cr1 and v_cr2 . By tracking the leaf marker point, various morphological parameters were calculated, including the bending angle of the petiole, the wind deflection angle, and the twist angle of leaves under different air velocities. When v_cr1 ≤v ≤v_cr2 , the parameters changed periodically. When v< v_cr1 , the petiole and the leaf bent statically, and the bending angle of the petiole and the wind deflection angle of the leaf gradually increased. When v >v_cr2 , the morphology of the leaf and the petiole was stable. Besides, this study tracked and measured the wind deflection area of leaf, which was consistent with the theoretical calculation results. The measurement of the leaf morphological parameters can reflect the morphological changes of leaves under airflow, thus providing a basis for the decision-making of air-assisted spray airflow.

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library,IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

The biomechanics of leaf oscillations during rainfall events

Plants are dynamic systems during rainfall events. As raindrops splash on leaf surfaces, the momentum of the raindrop is transferred to the leaf, causing the leaf to oscillate. The emphasis of this review is on the general principles of leaf oscillation models after raindrop impact and the ecological importance. Various leaf oscillation models and the underlying physical properties from biomechanics theory are highlighted. Additionally, we review experimental methods to derive the model parameters for and explore advances in our understanding of the raindrop-leaf impact process.

Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance

Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.

A semi-automated finite difference mesh creation method for use with immersed boundary software IB2d and IBAMR

Numerous fluid-structure interaction problems in biology have been investigated using the immersed boundary method. The advantage of this method is that complex geometries, e.g., internal or external morphology, can easily be handled without the need to generate matching grids for both the fluid and the structure. Consequently, the difficulty of modeling the structure lies often in discretizing the boundary of the complex geometry (morphology). Both commercial and open source mesh generators for finite element methods have long been established; however, the traditional immersed boundary method is based on a finite difference discretization of the structure. Here we present a software library for obtaining finite difference discretizations of boundaries for direct use in the 2D immersed boundary method. This library provides tools for extracting such boundaries as discrete mesh points from digital images. We give several examples of how the method can be applied that include passing flow through the veins of insect wings, within lymphatic capillaries, and around starfish using open-source immersed boundary software.

Intermittent sliding locomotion of a two-link body

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.

Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments

The movement of plankton is often dictated by local flow patterns, particularly during storms and in environments with strong flows. Reefs, macrophyte beds, and other immersed structures can provide shelter against washout and drastically alter the distributions of plankton as these structures redirect and slow the flows through them. Advection-diffusion and agent-based models are often used to describe the movement of plankton within marine and fresh water environments and across multiple scales. Experimental validation of such models of plankton movement within complex flow environments is challenging because of the difference in both time and spatial scales. Organisms on the scale of 1 mm or less swim by beating their appendages on the order of 1 Hz and are advected meters to kilometers over days, weeks, and months. One approach to study this challenging multiscale problem is to insert actively moving agents within a background flow field. Open source tools to implement this sort of approach are, however, limited. In this paper, we combine experiments and computational fluid dynamics with a newly developed agent-based modeling platform to quantify plankton movement at the scale of tens of centimeters. We use Artemia spp., or brine shrimp, as a model organism given their availability and ease of culturing. The distribution of brine shrimp over time was recorded in a flow tank with simplified physical models of macrophytes. These simplified macrophyte models were 3D-printed arrays of cylinders of varying heights and densities. Artemia nauplii were injected within these arrays, and their distributions over time were recorded with video. The detailed three-dimensional flow fields were quantified using computational fluid dynamics and validated experimentally with particle image velocimetry. To better quantify plankton distributions, we developed an agent-based modeling framework, Planktos, to simulate the movement of plankton immersed within such flow fields. The spatially and temporally varying Artemia distributions were compared across models of varying heights and densities for both the experiments and the agent-based models. The results show that increasing the density of the macrophyte bed drastically increases the average time it takes the plankton to be swept downstream. The height of the macrophyte bed had less of an effect. These effects were easily observed in both experimental studies and in the agent-based simulations.

Foliage motion under wind, from leaf flutter to branch buffeting

The wind-induced motion of the foliage in a tree is an important phenomenon both for biological issues (photosynthesis, pathogens development or herbivory) and for more subtle effects such as on wi-fi transmission or animal communication. Such foliage motion results from a combination of the motion of the branches that support the leaves, and of the motion of the leaves relative to the branches. Individual leaf dynamics relative to the branch, and branch dynamics have usually been studied separately. Here, in an experimental study on a whole tree in a large-scale wind tunnel, we present the first empirical evidence that foliage motion is actually dominated by individual leaf flutter at low wind velocities, and by branch turbulence buffeting responses at higher velocities. The transition between the two regimes is related to a weak dependence of leaf flutter on wind velocity, while branch turbulent buffeting is strongly dependent on it. Quantitative comparisons with existing engineering-based models of leaf and branch motion confirm the prevalence of these two mechanisms. Simultaneous measurements of the wind-induced drag on the tree and of the light interception by the foliage show the role of an additional mechanism, reconfiguration, whereby leaves bend and overlap, limiting individual leaf flutter. We then discuss the consequences of these findings on the role of wind-mediated phenomena.

Lift and Drag Acting on the Shell of the American Horseshoe Crab (Limulus polyphemus)

The intertidal zone is a turbulent landscape where organisms face numerous mechanical challenges from powerful waves. A model for understanding the solutions to these physical problems, the American horseshoe crab (Limulus polyphemus), is a marine arthropod that mates in the intertidal zone, where it must contend with strong ambient flows to maintain its orientation during locomotion and reproduction. Possible strategies to maintain position include either negative lift generation or the minimization of positive lift in flow. To quantify flow over the shell and the forces generated, we laser-scanned the 3D shape of a horseshoe crab, and the resulting digital reconstruction was used to 3D-print a physical model. We then recorded the movement of tracking particles around the shell model with high-speed video and analyzed the time-lapse series using particle image velocimetry (PIV). The velocity vector fields from PIV were used to validate numerical simulations performed with the immersed boundary (IB) method. IB simulations allowed us to resolve the forces acting on the shell, as well as the local three-dimensional flow velocities and pressures. Both IB simulations and PIV analysis of vorticity and velocity at a flow speed of 13 cm/s show negative lift for negative and zero angles of attack, and positive lift for positive angles of attack in a free-stream environment. In shear flow simulations, we found near-zero lift for all orientations tested. Because horseshoe crabs are likely to be found primarily at near-zero angles of attack, we suggest that this negative lift helps maintain the orientation of the crab during locomotion and mating. This study provides a preliminary foundation for assessing the relationship between documented morphological variation and potential environmental variation for distinct populations of horseshoe crabs along the Atlantic Coast. It also motivates future studies which could consider the stability of the horseshoe crab in unsteady, oscillating flows.

Plant vibrations at all scales: a review

Plant vibrations is a wide subject that covers topics ranging from the swaying of trees under wind to elastic waves made by an insect on a leaf to communicate with its neighbors. For this reason, the state of the art is somehow fragmented over several communities. This review aims at giving a general overview of the main results and challenges in plant vibrations. Several scales are considered, from the very small and local, in leaves or fruits, to large canopies of many plants.

Mechanics of a plant in fluid flow

Plants live in constantly moving fluid, whether air or water. In response to the loads associated with fluid motion, plants bend and twist, often with great amplitude. These large deformations are not found in traditional engineering application and thus necessitate new specialized scientific developments. Studying fluid-structure interaction (FSI) in botany, forestry, and agricultural science is crucial to the optimization of biomass production for food, energy, and construction materials. FSIs are also central in the study of the ecological adaptation of plants to their environment. This review paper surveys the mechanics of FSI on individual plants. I present a short refresher on fluid mechanics then dive into the statics and dynamics of plant-fluid interactions. For every phenomenon considered, I examine the appropriate dimensionless numbers to characterize the problem, discuss the implications of these phenomena on biological processes, and propose future research avenues. I cover the concept of reconfiguration while considering poroelasticity, torsion, chirality, buoyancy, and skin friction. I also assess the dynamical phenomena of wave action, flutter, and vortex-induced vibrations.

Life in the flow: unique adaptations for feeding on drifting zooplankton in garden eels

A major challenge faced by sessile animals that feed in the flow is to maintain effective feeding postures while enduring hydrodynamic forces. Garden eels exhibit an exceptional lifestyle: feeding on drifting zooplankton while being 'anchored' in a burrow they dig in the sand. Using underwater observations, sampling and three-dimensional video recording, we measured the feeding rates and characterized feeding postures of garden eels under a wide range of current speeds. We show that the eels behaviorally resolve the trade-off between adverse biomechanical forces and beneficial fluxes of food by modulating their body postures according to current speeds. In doing so, the eels substantially reduce drag forces when currents are strong, yet keep their head well above bottom in order to effectively feed under conditions of high prey fluxes. These abilities have allowed garden eels to become one of the rare oceanic fishes that live in sandy, predation-rich habitats and feed on zooplankton while being attached to the bottom.

Does flutter prevent drag reduction by reconfiguration?

The static reconfiguration of flexible beams exposed to transverse flows is classically known to reduce the drag these structures have to withstand. But the more a structure bends, the more parallel to the flow it becomes, and flexible beams in axial flows are prone to a flutter instability that is responsible for large inertial forces that drastically increase their drag. It is, therefore, unclear whether flexibility would still alleviate, or on the contrary enhance, the drag when flapping occurs on a reconfiguring structure. In this article, we perform numerical simulations based on reduced-order models to demonstrate that the additional drag induced by the flapping motion is almost never significant enough to offset the drag reduction due to reconfiguration. Isolated and brief snapping events may transiently raise the drag above that of a rigid structure in the particular case of heavy, moderately slender beams. But apart from these short peak events, the drag force remains otherwise always significantly reduced in comparison with a rigid structure.

Herbivores alter plant-wind interactions by acting as a point mass on leaves and by removing leaf tissue

In nature, plants regularly interact with herbivores and with wind. Herbivores can wound and alter the structure of plants, whereas wind can exert aerodynamic forces that cause the plants to flutter or sway. While herbivory has many negative consequences for plants, fluttering in wind can be beneficial for plants by facilitating gas exchange and loss of excess heat. Little is known about how herbivores affect plant motion in wind. We tested how the mass of an herbivore resting on a broad leaf of the tulip tree Liriodendron tulipifera, and the damage caused by herbivores, affected the motion of the leaf in wind. For this, we placed mimics of herbivores on the leaves, varying each herbivore's mass or position, and used high-speed video to measure how the herbivore mimics affected leaf movement and reconfiguration at two wind speeds inside a laboratory wind tunnel. In a similar setup, we tested how naturally occurring herbivore damage on the leaves affected leaf movement and reconfiguration. We found that the mass of an herbivore resting on a leaf can change that leaf's orientation relative to the wind and interfere with the ability of the leaf to reconfigure into a smaller, more streamlined shape. A large herbivore load slowed the leaf's fluttering frequency, while naturally occurring damage from herbivores increased the leaf's fluttering frequency. We conclude that herbivores can alter the physical interactions between wind and plants by two methods: (1) acting as a point mass on the plant while it is feeding and (2) removing tissue from the plant. Altering a plant's interaction with wind can have physical and physiological consequences for the plant. Thus, future studies of plants in nature should consider the effect of herbivory on plant-wind interactions, and vice versa.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Smoothed particle hydrodynamics and element bending group modeling of flexible fibers interacting with viscous fluids

This paper presents a smoothed particle hydrodynamics (SPH) and element bending group (EBG) coupling method for modeling the interaction of flexible fibers with moving viscous fluids. SPH is a well-developed mesh-free particle method for simulating viscous fluid flows. EBG is also a particle method for modeling flexible bodies. The interaction of flexible fibers with moving viscous fluids is rendered through the interaction of EBG particles for flexible fiber and SPH particles for fluid. In numerical simulation, flexible fibers of different lengths are immersed in a moving viscous fluid driven by a body force. The drag force on the fiber obtained from SPH-EBG simulation agrees well with experimental observations. It is shown that the flexible fiber demonstrates three typical bending modes, including the U-shaped mode, the flapping mode, and the closed mode, and that the flexible fiber experiences a drag reduction due to its reconfiguration by bending. It is also found that the U4/3 drag scaling law for a flexible fiber is only valid for the U-shaped mode, but not valid for the flapping and closed modes. The results indicate that the reconfiguration of a flexible fiber is caused by the fluid force acting on it, while vortex shedding is of importance in the translations of bending modes.

Clap and fling mechanism with interacting porous wings in tiny insect flight

The aerodynamics of flapping flight for the smallest insects such as thrips is often characterized by a 'clap and fling' of the wings at the end of the upstroke and the beginning of the downstroke. These insects fly at Reynolds numbers (Re) on the order of 10 or less where viscous effects are significant. Although this wing motion is known to augment the lift generated during flight, the drag required to fling the wings apart at this scale is an order of magnitude larger than the corresponding force acting on a single wing. Since the opposing forces acting normal to each wing nearly cancel during the fling, these large forces do not have a clear aerodynamic benefit. If flight efficiency is defined as the ratio of lift to drag, the 'clap and fling' motion dramatically reduces efficiency relative to the case of wings that do not aerodynamically interact. In this paper, the effect of a bristled wing characteristic of many of these insects is investigated using computational fluid dynamics. We perform 2D numerical simulations using a porous version of the immersed boundary method. Given the computational complexity involved in modeling flow through exact descriptions of bristled wings, the wing is modeled as a homogenous porous layer as a first approximation. High-speed video recordings of free flying thrips in take-off flight were captured in the laboratory, and an analysis of the wing kinematics was performed. This information was used for the estimation of input parameters for the simulations. As compared to a solid wing (without bristles), the results of the study show that the porous nature of the wings contributes largely to drag reduction across the Re range explored. The aerodynamic efficiency, calculated as the ratio of lift to drag coefficients, was larger for some porosities when compared to solid wings.