Mathematical modeling, immersed boundary simulation, and experimental validation of the fluid flow around the upside-down jellyfish Cassiopea xamachana

The jellyfish has been the subject of extensive research in the areas of ecology, biomechanics, fluid dynamics and engineering. Previous mathematical and experimental studies of the flows generated by jellyfish focused primarily on swimming mechanisms. Recently, the fluid dynamics of feeding from currents generated during swimming has been considered. In this study the benthic lifestyle of the upside- down jellyfish Cassiopea xamachana was capitalized upon to explore the fluid dynamics of feeding uncoupled from swimming. A two-dimensional mathematical model was developed to capture the fundamental characteristics of the motion of the unique concave bell shape. Given the prominence of the oral arm array, this structure was included and modeled as a porous layer that perturbs the flow generated by bell contractions. The immersed boundary method was used to solve the fluid-structure interaction problem. Parameter sweeps were used to explore numerically the effects of changes in pulse dynamics and the properties of the oral arms independently. Velocity fields obtained from live organisms using digital particle image velocimetry were used to validate the numerical simulations of the model. Parameter sweeps were used to explore the effects of scaling and to compare the model to a more traditional bell-only model. The effects of low-velocity background flow, neighboring jellyfish, and synchronous and asynchronous pulsing were also examined. The presence of the prominent porous layer structure in the field of flow increased the flux of new fluid from along the substrate to the bell. A consistent pattern of flow across the porous layer across a wide range of background flow patterns. The numerical simulations showed that pauses between bell expansion and the next contraction altered fluid flow over the bell and through the oral arms. Studies of the effects of neighboring models showed that spacing and relative size of individuals changed flow rates substantially. These substantial changes could explain so-called hitchhiking behavior observed in smaller or weakened jellyfish

Flow Structure and Transport Characteristics of Feeding and Exchange Currents Generated by Upside-Down Cassiopea Jellyfish

Quantifying the flows generated by the pulsations of jellyfish bells is crucial for understanding the mechanics and efficiency of their swimming and feeding. Recent experimental and theoretical work has focused on the dynamics of vortices in the wakes of swimming jellyfish with relatively simple oral arms and tentacles. The significance of bell pulsations for generating feeding currents through elaborate oral arms and the consequences for particle capture are not as well understood. To isolate the generation of feeding currents from swimming, the pulsing kinematics and fluid flow around the benthic jellyfish Cassiopea spp. were investigated using a combination of videography, digital particle image velocimetry and direct numerical simulation. During the rapid contraction phase of the bell, fluid is pulled into a starting vortex ring that translates through the oral arms with peak velocities that can be of the order of 10 cm s–1. Strong shear flows are also generated across the top of the oral arms throughout the entire pulse cycle. A coherent train of vortex rings is not observed, unlike in the case of swimming oblate medusae such as Aurelia aurita. The phase-averaged flow generated by bell pulsations is similar to a vertical jet, with induced flow velocities averaged over the cycle of the order of 1–10 mm s–1. This introduces a strong near-horizontal entrainment of the fluid along the substrate and towards the oral arms. Continual flow along the substrate towards the jellyfish is reproduced by numerical simulations that model the oral arms as a porous Brinkman layer of finite thickness. This two-dimensional numerical model does not, however, capture the far-field flow above the medusa, suggesting that either the three-dimensionality or the complex structure of the oral arms helps to direct flow towards the central axis and up and away from the animal

Three-dimensional low Reynolds number flows near biological filtering and protective layers

Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to many animals and plants. Trichomes (the hairs or fine outgrowths on plants) can drastically alter both the average wind speed and profile near the leaf's surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the 3D flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate that the flow can be highly 3D with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows.Comment: 28 pages, 10 figure

Feeding Currents Generated by Upside Down Jellyfish

We present fluid dynamics videos of the pulsing dynamics and the resulting fluid flow generated by the upside down jellyfish, Cassiopea spp. Medusae of this genus are unusual in that they typically rest upside down on the ocean floor and pulse their bells to generate feeding currents, only swimming when significantly disturbed. The pulsing kinematics and fluid flow around these upside down jellyfish is investigated using a combination of videography, flow visualization, and numerical simulation. Significant mixing occurs around and directly above the oral arms and secondary mouths. Numerical simulations using the immersed boundary method with a porous layer representing the oral arms agree with the experimental results. The simulations also suggest that the presence of porous oral arms induce net horizontal flow towards the bell. Coherent vortex rings are not seen in the wake above the jellyfish, but starting and stopping vortices are observed before breaking up as they pass through the elaborate oral arms (if extended).Comment: 3 pages, 2 movie

A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfish Cassiopea xamachana

Mathematical and experimental studies of the flows generated by jellyfish have focused primarily on mechanisms of swimming. More recent work has also considered the fluid dynamics of feeding from currents generated during swimming. Here we capitalize on the benthic lifestyle of the upside-down jellyfish

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

Flexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. In strong winds and flood waters, for example, leaves roll up into cone shapes that reduce drag compared with rigid objects of similar surface area. Less understood is how a leaf attached to a flexible leaf stalk will roll up stably in an unsteady flow. Previous mathematical and physical models have only considered the case of a flexible sheet attached to a rigid tether in steady flow. In this paper, the dynamics of the flow around the leaf of the wild ginge

BioEarth: Envisioning and developing a new regional earth system model to inform natural and agricultural resource management

As managers of agricultural and natural resources are confronted with uncertainties in global change impacts, the complexities associated with the interconnected cycling of nitrogen, carbon, and water present daunting management challenges. Existing models provide detailed information on specific sub-systems (e.g., land, air, water, and economics). An increasing awareness of the unintended consequences of management decisions resulting from interconnectedness of these sub-systems, however, necessitates coupled regional earth system models (EaSMs). Decision makers’ needs and priorities can be integrated into the model design and development processes to enhance decision-making relevance and “usability” of EaSMs. BioEarth is a research initiative currently under development with a focus on the U.S. Pacific Northwest region that explores the coupling of multiple stand-alone EaSMs to generate usable information for resource decision-making. Direct engagement between model developers and non-academic stakeholders involved in resource and environmental management decisions throughout the model development process is a critical component of this effort. BioEarth utilizes a bottom-up approach for its land surface model that preserves fine spatial-scale sensitivities and lateral hydrologic connectivity, which makes it unique among many regional EaSMs. This paper describes the BioEarth initiative and highlights opportunities and challenges associated with coupling multiple stand-alone models to generate usable information for agricultural and natural resource decision-making