Jifeng Peng

Transport of inertial particles by Lagrangian coherent structures : application to predator-prey interaction in jellyfish feeding

We use a dynamical systems approach to identify coherent structures from often chaotic motions of inertial particles in open flows. We show that particle Lagrangian coherent structures (pLCS) act as boundaries between regions in which particles have different kinematics. They provide direct geometric information about the motion of ensembles of inertial particles, which is helpful to understand their transport. As an application, we apply the methodology to a planktonic predator–prey system in which moon jellyfish Aurelia aurita uses its body motion to generate a flow that transports small plankton such as copepods to its vicinity for feeding. With the flow field generated by the jellyfish measured experimentally and the dynamics of plankton described by a modified Maxey–Riley equation, we use the pLCS to identify a capture region in which prey can be captured by the jellyfish. The properties of the pLCS and the capture region enable analysis of the effect of several physiological and mechanical parameters on the predator–prey interaction, such as prey size, escape force, predator perception, etc. The methods developed here are equally applicable to multiphase and granular flows, and can be generalized to any other particle equation of motion, e.g. equations governing the motion of reacting particles or charged particles.

An overview of a Lagrangian method for analysis of animal wake dynamics

SUMMARY The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a Lagrangian approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the Eulerian perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available.

Geometry of unsteady fluid transport during fluid–structure interactions

We describe the application of tools from dynamical systems to define and quantify the unsteady fluid transport that occurs during fluid–structure interactions and in unsteady recirculating flows. The properties of Lagrangian coherent structures (LCS) are used to enable analysis of flows with arbitrary time-dependence, thereby extending previous analytical results for steady and time-periodic flows. The LCS kinematics are used to formulate a unique, physically motivated definition for fluid exchange surfaces and transport lobes in the flow. The methods are applied to numerical simulations of two-dimensional flow past a circular cylinder at a Reynolds number of 200; and to measurements of a freely swimming organism, the Aurelia aurita jellyfish. The former flow provides a canonical system in which to compare the present geometrical analysis with classical, Eulerian (e.g. vortex shedding) perspectives of fluid–structure interactions. The latter flow is used to deduce the physical coupling that exists between mass and momentum transport during self-propulsion. In both cases, the present methods reveal a well-defined, unsteady recirculation zone that is not apparent in the corresponding velocity or vorticity fields. Transport rates between the ambient flow and the recirculation zone are computed for both flows. Comparison of fluid transport geometry for the cylinder crossflow and the self-propelled swimmer within the context of existing theory for two-dimensional lobe dynamics enables qualitative localization of flow three-dimensionality based on the planar measurements. Benefits and limitations of the implemented methods are discussed, and some potential applications for flow control, unsteady propulsion, and biological fluid dynamics are proposed.

The 'upstream wake' of swimming and flying animals and its correlation with propulsive efficiency.

SUMMARY The interaction between swimming and flying animals and their fluid environments generates downstream wake structures such as vortices. In most studies, the upstream flow in front of the animal is neglected. In this study, we demonstrate the existence of upstream fluid structures even though the upstream flow is quiescent or possesses a uniform incoming velocity. Using a computational model, the flow generated by a swimmer (an oscillating flexible plate) is simulated and a new fluid mechanical analysis is applied to the flow to identify the upstream fluid structures. These upstream structures show the exact portion of fluid that is going to interact with the swimmer. A mass flow rate is then defined based on the upstream structures, and a metric for propulsive efficiency is established using the mass flow rate and the kinematics of the swimmer. We propose that the unsteady mass flow rate defined by the upstream fluid structures can be used as a metric to measure and objectively compare the efficiency of locomotion in water and air.

Instabilities on Prey Dynamics in Jellyfish Feeding

We study the dynamics of plankton in the wake of a jellyfish. Using an analytical approach, we derive a reduced-order equation that governs the prey motion which is modeled as neutrally-buoyant inertial particle. This modified equation takes into account both the effects of prey inertia and self-propulsion and enables us to calculate both the attracting and repelling Lagrangian coherent structures for the prey motion. For the case of zero self-propulsion, it is simplified to the equation of motion for infinitesimal fluid particles. Additionally, we determine the critical size of prey over which instabilities on its motion occur resulting in different dynamics from those predicted by the reduced-order equation even for the case of zero self-propulsion. We illustrate our theoretical findings through an experimentally measured velocity field of a jellyfish. Using the inertial equation, we calculate the Lagrangian coherent structures that characterize prey motion as well as the instability regions over which larger prey will have different dynamics even for the case of zero self-propulsion.

A new approach to wind energy: Opportunities and challenges

Despite common characterizations of modern wind energy technology as mature, there remains a persistent disconnect between the vast global wind energy resource—which is 20 times greater than total global power consumption—and the limited penetration of existing wind energy technologies as a means for electricity generation worldwide. We describe an approach to wind energy harvesting that has the potential to resolve this disconnect by geographically distributing wind power generators in a manner that more closely mirrors the physical resource itself. To this end, technology development is focused on large arrays of small wind turbines that can harvest wind energy at low altitudes by using new concepts of biology-inspired engineering. This approach dramatically extends the reach of wind energy, as smaller wind turbines can be installed in many places that larger systems cannot, especially in built environments. Moreover, they have lower visual, acoustic, and radar signatures, and they may pose significantly less risk to birds and bats. These features can be leveraged to attain cultural acceptance and rapid adoption of this new technology, thereby enabling significantly faster achievement of state and national renewable energy targets than with existing technology alone. Favorable economics stem from an orders-of-magnitude reduction in the number of components in a new generation of simple, mass-manufacturable (even 3D-printable), vertical-axis wind turbines. However, this vision can only be achieved by overcoming significant scientific challenges that have limited progress over the past three decades. The following essay summarizes our approach as well as the opportunities and challenges associated with it, with the aim of motivating a concerted effort in basic and applied research in this area.

Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer.

In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion. The parameter space of body kinematics is explored through four quantities: a measure of body shape, stroke amplitude, the ratio between body contraction duration and extension duration, and the pulsing frequency. The effects of these parameters on thrust, input power requirement and circulation production are quantified. Two metrics, cruising speed and energy cost of locomotion, are used to evaluate the propulsion performance. The study finds that a more prolate-shaped swimmer with larger stroke amplitudes is able to swim faster, but its cost of locomotion is also higher. In contrast, a more oblate-shaped swimmer with smaller stroke amplitudes uses less energy for its locomotion, but swims more slowly. Compared with symmetric strokes with equal durations of contraction and extension, faster bell contractions increase the swimming speed whereas faster bell extensions decrease it, but both require a larger energy input. This study shows that besides the well-studied correlations between medusan body shape and locomotion, stroke variables also affect the propulsion performance. It provides a framework for comparing the propulsion performance of axisymmetric swimmers based on their body kinematics when it is difficult to measure and analyze their wakes empirically. The knowledge from this study is also useful for the design of robotic swimmers that use axisymmetric body contractions for propulsion.

Leapfrogging of two thick-cored vortex rings

Leapfrogging of two vortex rings of thick cores is studied in laboratory experiments. Quantitative flow measurements show that, during leapfrogging, vorticity at the outer portion of the two cores diffuses together. However, the two cores remain clearly differentiable with distinct peaks. Vortex circulation decreases at a faster rate when the two rings are aligned radially and the passing ring is closer to axis touching due to vorticity cancellation. When two consecutive passages occur, vorticity cancellation is reduced in the second passage because the passing ring is further away from axis touching compared with that in the first passage. The study also finds that when the interval between generations of two rings is small, the front ring strongly influences the formation of the rear ring, whose core has an elongated tail of vorticity on its formation. The rear ring later sheds vorticity, whose amount increases with a smaller initial separation. The shedded vorticity, when strong enough, counters the effect of the front ring and prevents leapfrogging.

An Experimental Investigation of Mode Shift of Cantilever Flexible Plate Coupled with Fluid

Abstract The vibration of a structure coupled with liquid is an important problem that has many significant engineering applications such as the bionics of flapping fin, harvest of tide energy, and the conventional areas of marine and offshore structures. It is critical to experimentally validate the dynamic parameters of structures coupled with fluid so as to accurately and efficiently model, design and develop related engineering systems. This paper presents an experimental study to quantify the shifts of multiple modes of cantilever flexible plate under water due to hydrodynamics effects. This goal is accomplished by using free-decay response measurement of a cantilever flexible plate exposed in air and submerged in water. Free-decay responses are used to identify the plate dynamic properties. The FFT, power spectrum, spectrogram, empirical modal decomposition are used to quantify plate spectrum signatures. The hydrodynamic effects of liquid on the natural frequencies and the damping of plates are characterized. A comparison between the power spectra of response and empirical mode shows a good correlation. The nonlinear hydrodynamic effects on the plate response are also discussed based on experimental results.