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

Toward empirical evaluation of left ventricle function: A novel mathematical mapping

A strategy is developed to facilitate quantitative analysis of left ventricle morphology based on clinically measured surface geometry and muscle fiber patterns rather than lower order geometric approximations previously required. A transfer function is derived which maps measured three-dimensional ventricle surfaces and associated muscle fiber patterns to a right circular cylinder, while preserving characteristic kinematics of the system. Functional analysis of ventricular morphology at various stages of the cardiac cycle proceeds by using classical methods on the cylindrical ventricle model, with substantially reduced analytical complexity when compared to similar calculations on the real ventricle shape. Functional morphology of the real ventricle shape at any stage of the cardiac cycle is subsequently deduced by applying the inverse of the transfer function in order to map the computed right circular cylinder back to its corresponding real ventricle shape. Limitations of the method are discussed in the context of real left ventricle performance, and extension of the method for analysis of functional morphology in other biomechanical systems is explored

Transport and stirring induced by vortex formation

The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper

Power-generation enhancements and upstream flow properties of turbines in unsteady inflow conditions

Energy-harvesting systems in complex flow environments, such as floating offshore wind turbines, tidal turbines, and ground-fixed turbines in axial gusts, encounter unsteady streamwise flow conditions that affect their power generation and structural loads. In some cases, enhancements in time-averaged power generation above the steady-flow operating point are observed. To characterize these dynamics, a nonlinear dynamical model for the rotation rate and power extraction of a periodically surging turbine is derived and connected to two potential-flow representations of the induction zone upstream of the turbine. The model predictions for the time-averaged power extraction of the turbine and the upstream flow velocity and pressure are compared against data from experiments conducted with a surging-turbine apparatus in an open-circuit wind tunnel at a diameter-based Reynolds number of $Re_D = 6.3\times10^5$ and surge-velocity amplitudes of up to 24% of the wind speed. The combined modeling approach captures trends in both the time-averaged power extraction and the fluctuations in upstream flow quantities, while relying only on data from steady-flow measurements. The sensitivity of the observed increases in time-averaged power to steady-flow turbine characteristics is established, thus clarifying the conditions under which these enhancements are possible. Finally, the influence of unsteady fluid mechanics on time-averaged power extraction is explored analytically. The theoretical framework and experimental validation provide a cohesive modeling approach that can drive the design, control, and optimization of turbines in unsteady flow conditions, as well as inform the development of novel energy-harvesting systems that can leverage unsteady flows for large increases in power-generation capacities.Comment: 36 pages, 19 figures. Currently under revie

Phenotypic Plasticity in Juvenile Jellyfish Medusae Facilitates Effective Animal–Fluid Interaction

Locomotion and feeding in marine animals are intimately linked to the flow dynamics created by specialized body parts. This interaction is of particular importance during ontogeny, when changes in behaviour and scale challenge the organism with shifts in fluid regimes and altered functionality. Previous studies have indicated that Scyphozoan jellyfish ontogeny accommodates the changes in fluid dynamics associated with increasing body dimensions and velocities during development. However, in addition to scale and behaviour that—to a certain degree—underlie the control of the animal, flow dynamics are also dependent on external factors such as temperature. Here, we show phenotypic plasticity in juvenile Aurelia aurita medusae, where morphogenesis is adapted to altered fluid regimes imposed by changes in ambient temperature. In particular, differential proportional growth was found to compensate for temperature-dependent changes in viscous effects, enabling the animal to use adhering water boundary layers as ‘paddles’—and thus economize tissue—at low temperatures, while switching to tissue-dominated propulsion at higher temperatures where the boundary layer thickness is insufficient to serve for paddling. This effect was predicted by a model of animal–fluid interaction and confirmed empirically by flow-field visualization and assays of propulsion efficiency

Functional Morphology and Fluid Interactions During Early Development of the Scyphomedusa Aurelia aurita

Scyphomedusae undergo a predictable ontogenetic transition from a conserved, universal larval form to a diverse array of adult morphologies. This transition entails a change in bell morphology from a highly discontinuous ephyral form, with deep clefts separating eight discrete lappets, to a continuous solid umbrella-like adult form. We used a combination of kinematic, modeling, and flow visualization techniques to examine the function of the medusan bell throughout the developmental changes of the scyphomedusa Aurelia aurita. We found that flow around swimming ephyrae and their lappets was relatively viscous (1 < Re < 10) and, as a result, ephyral lappets were surrounded by thick, overlapping boundary layers that occluded flow through the gaps between lappets. As medusae grew, their fluid environment became increasingly influenced by inertial forces (10 < Re < 10,000) and, simultaneously, clefts between the lappets were replaced by organic tissue. Hence, although the bell undergoes a structural transition from discontinuous (lappets with gaps) to continuous (solid bell) surfaces during development, all developmental stages maintain functionally continuous paddling surfaces. This developmental pattern enables ephyrae to efficiently allocate tissue to bell diameter increase via lappet growth, while minimizing tissue allocation to inter-lappet spaces that maintain paddle function due to boundary layer overlap

Passive Energy Recapture in Jellyfish Contributes to Propulsive Advantage over other Metazoans

Gelatinous zooplankton populations are well known for their ability to take over perturbed ecosystems. The ability of these animals to outcompete and functionally replace fish that exhibit an effective visual predatory mode is counterintuitive because jellyfish are described as inefficient swimmers that must rely on direct contact with prey to feed. We show that jellyfish exhibit a unique mechanism of passive energy recapture, which is exploited to allow them to travel 30% further each swimming cycle, thereby reducing metabolic energy demand by swimming muscles. By accounting for large interspecific differences in net metabolic rates, we demonstrate, contrary to prevailing views, that the jellyfish (Aurelia aurita) is one of the most energetically efficient propulsors on the planet, exhibiting a cost of transport (joules per kilogram per meter) lower than other metazoans. We estimate that reduced metabolic demand by passive energy recapture improves the cost of transport by 48%, allowing jellyfish to achieve the large sizes required for sufficient prey encounters. Pressure calculations, using both computational fluid dynamics and a newly developed method from empirical velocity field measurements, demonstrate that this extra thrust results from positive pressure created by a vortex ring underneath the bell during the refilling phase of swimming. These results demonstrate a physical basis for the ecological success of medusan swimmers despite their simple body plan. Results from this study also have implications for bioinspired design, where low-energy propulsion is required

Three-Dimensional Velocity Measurements Around and Downstream of a Rotating Vertical Axis Wind Turbine

Modern designs for straight-bladed vertical axis wind turbines (VAWTs) feature smaller individual footprints than conventional horizontal axis wind turbines (HAWTs), allowing closer spacing of turbines and potentially greater power extraction for the same wind farm footprint. However, the wakes of upstream turbines could persist far enough to affect the performance of closely-spaced downstream turbines. In order to optimize the inter-turbine spacing and to investigate the potential for constructive aerodynamic interactions, the complex dynamics of VAWT wakes should be understood. The full three-component mean velocity field around and downstream of a scaled model of a rotating VAWT has been measured by Magnetic Resonance Velocimetry (MRV). The model turbine has an aspect ratio (height/diameter) of 1, and was operated in a water facility at subscale but still turbulent Reynolds number of 11,600 based on the turbine diameter. The main flow features including recirculation bubble sizes and strong vortex structures are believed to be representative of flow at full scale Reynolds number. To have kinematic similarity with a power-producing turbine, the model turbine was externally driven. Measurements were taken with the turbine stationary and while driven at tip speed ratios (TSRs) of 1.25 and 2.5, realistic values for VAWTs in operation. The MRV measurement produced three-dimensional velocity data with a resolution of 1/50 of the turbine diameter in all three directions. The flow is shown to be highly three dimensional and asymmetric for the entirety of the investigated region (up to 7 diameters downstream of the turbine). The higher TSR produced greater velocity defect and asymmetry in the near wake behind the turbine, but also showed faster wake recovery than the slower TSR and stationary cases. Wake recovery is affected by a counter-rotating vortex pair generated at the upwind-turning side of the turbine, which mixes faster fluid from the free stream in with the wake. The strength of vortices is shown to increase with TSR

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-of-plane effects. Particle image velocimetry measurements of a freely swimming jellyfish medusa and a freely swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data