Sensitivity analysis of kinematic approximations in dynamic medusan swimming models

Hydrodynamic Interaction of Two Self-Propelled Fish Swimming in a Tandem Arrangement

Collective locomotion in biological systems is ubiquitous and attracts much attention, and there are complex hydrodynamics involved. The hydrodynamic interaction for fish schooling is examined using two-dimensional numerical simulations of a pair of self-propelled swimming fish in this paper. The effects of different parameters on swimming speed gain and energy-saving efficiency are investigated by adjusting swimming parameters (initial separation distance d0, tail beat amplitude A, body wavelength λ, and period of oscillation T) at different phase difference δϕ between two fish. The hydrodynamic interaction performance of fish swimming in a tandem arrangement is analyzed with the help of the instantaneous vorticity contours, pressure contours, and mean work done. Using elementary hydrodynamic arguments, a unifying mechanistic principle, which characterizes the fish locomotion by deriving a scaling relation that links swimming speed u to body kinematics (A, T, and λ), arrangement of formation (d0), and fluid properties (kinematic viscosity ν), is revealed. It is shown that there are some certain scaling laws between similarity criterion number (Reynolds number (Re) and Strouhal number (St)) and energy-consuming coefficient (CE) under different parameters (Δ). In particular, a generality in the relationships of St–Re and CE–(Re ·Δ) can emerge despite significant disparities in locomotory performance.

Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle

Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their bell kinematics coupled with their morphological, muscular, material properties. We investigated jellyfish locomotion by conducting in silico comparative studies and explored swimming performance across different fluid scales (i.e., Reynolds Number), bell contraction frequencies, and contraction phase kinematics (duty cycle) for a jellyfish with a fineness ratio of 1 (ratio of bell height to bell diameter). To study these relationships, an open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of a flexible jellyfish bell in a viscous fluid. Thorough 2D parameter subspace explorations illustrated optimal parameter combinations in which give rise to enhanced swimming performance. All performance metrics indicated a higher sensitivity to bell actuation frequency than fluid scale or duty cycle, via Sobol sensitivity analysis, on a higher performance parameter subspace. Moreover, Pareto-like fronts were identified in the overall performance space involving the cost of transport and forward swimming speed. Patterns emerged within these performance spaces when highlighting different parameter regions, which complemented the global sensitivity results. Lastly, an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.

Cool your jets: biological jet propulsion in marine invertebrates

Pulsatile jet propulsion is a common swimming mode used by a diverse array of aquatic taxa from chordates to cnidarians. This mode of locomotion has interested both biologists and engineers for over a century. A central issue to understanding the important features of jet-propelling animals is to determine how the animal interacts with the surrounding fluid. Much of our knowledge of aquatic jet propulsion has come from simple theoretical approximations of both propulsive and resistive forces. Although these models and basic kinematic measurements have contributed greatly, they alone cannot provide the detailed information needed for a comprehensive, mechanistic overview of how jet propulsion functions across multiple taxa, size scales and through development. However, more recently, novel experimental tools such as high-speed 2D and 3D particle image velocimetry have permitted detailed quantification of the fluid dynamics of aquatic jet propulsion. Here, we provide a comparative analysis of a variety of parameters such as efficiency, kinematics and jet parameters, and review how they can aid our understanding of the principles of aquatic jet propulsion. Research on disparate taxa allows comparison of the similarities and differences between them and contributes to a more robust understanding of aquatic jet propulsion.

Cyanea capillata bell kinematics analysis through corrected in situ imaging and modeling using strategic discretization techniques

Obtaining accurate kinematic data of animals is essential for many biological studies and bio-inspired engineering. Many animals, however, are either too large or too delicate to transport to controlled environments where accurate kinematic data can be easily obtained. Often, in situ recordings are the only means available but are often subject to multi-axis motion and relative magnification changes with time leading to large discrepancies in the animal kinematics. Techniques to compensate for these artifacts were applied to a large jellyfish, Cyanea capillata, freely swimming in ocean waters. The bell kinematics were captured by digitizing exumbrella profiles for two full swimming cycles. Magnification was accounted for by tracking a reference point on the ocean floor and by observing the C. capillata exumbrella arclength in order to have a constant scale through the swimming cycles. A linear fit of the top bell section was used to find the body angle with respect to the camera coordinate system. Bell margin trajectories over two swimming cycles confirmed the accuracy of the correction techniques. The corrected profiles were filtered and interpolated to provide a set of time-dependent points along the bell. Discrete models of the exumbrella were used to analyze the bell kinematics. Exumbrella discretization was conducted using three different methods. Fourier series were fitted to the discretized models and subsequently used to analyze the bell kinematics of the C. capillata. The analysis showed that the bell did not deform uniformly over time with different segments lagging behind each other. Looping of the bell trajectory between contraction and relaxation was also present through most of the exumbrella. The bell margin had the largest looping with an outer path during contraction and inner path during relaxation. The subumbrella volume was approximated based on the exumbrella kinematics and was found to increase during contraction.

Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake

Fast-swimming hydromedusan jellyfish possess a characteristic funnel-shaped velum at the exit of their oral cavity that interacts with the pulsed jets of water ejected during swimming motions. It has been previously assumed that the velum primarily serves to augment swimming thrust by constricting the ejected flow in order to produce higher jet velocities. This paper presents high-speed video and dye-flow visualizations of free-swimming Nemopsis bachei hydromedusae, which instead indicate that the time-dependent velar kinematics observed during the swimming cycle primarily serve to optimize vortices formed by the ejected water rather than to affect the speed of the ejected flow. Optimal vortex formation is favorable in fast-swimming jellyfish because,unlike the jet funnelling mechanism, it allows for the minimization of energy costs while maximizing thrust forces. However, the vortex `formation number'corresponding to optimality in N. bachei is substantially greater than the value of 4 found in previous engineering studies of pulsed jets from rigid tubes. The increased optimal vortex formation number is attributable to the transient velar kinematics exhibited by the animals. A recently developed model for instantaneous forces generated during swimming motions is implemented to demonstrate that transient velar kinematics are required in order to achieve the measured swimming trajectories. The presence of velar structures in fast-swimming jellyfish and the occurrence of similar jet-regulating mechanisms in other jet-propelled swimmers (e.g. the funnel of squid) appear to be a primary factor contributing to success of fast-swimming jetters, despite their primitive body plans.

Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses

Flow patterns generated by medusan swimmers such as jellyfish are known to differ according the morphology of the various animal species. Oblate medusae have been previously observed to generate vortex ring structures during the propulsive cycle. Owing to the inherent physical coupling between locomotor and feeding structures in these animals, the dynamics of vortex ring formation must be robustly tuned to facilitate effective functioning of both systems. To understand how this is achieved, we employed dye visualization techniques on scyphomedusae (Aurelia aurita) observed swimming in their natural marine habitat. The flow created during each propulsive cycle consists of a toroidal starting vortex formed during the power swimming stroke, followed by a stopping vortex of opposite rotational sense generated during the recovery stroke. These two vortices merge in a laterally oriented vortex superstructure that induces flow both toward the subumbrellar feeding surfaces and downstream. The lateral vortex motif discovered here appears to be critical to the dual function of the medusa bell as a flow source for feeding and propulsion. Furthermore, vortices in the animal wake have a greater volume and closer spacing than predicted by prevailing models of medusan swimming. These effects are shown to be advantageous for feeding and swimming performance, and are an important consequence of vortex interactions that have been previously neglected.