Lagrangian coherent structures

Jellyfish have provided insight into important components of animal propulsion, such as suction thrust, passive energy recapture, vortex wall effects, and the rotational mechanics of turning. These traits are critically important to jellyfish because they must propel themselves despite severe limitations on force production imposed by rudimentary cnidarian muscular structures. Consequently, jellyfish swimming can occur only by careful orchestration of fluid interactions. Yet these mechanics may be more broadly instructive because they also characterize processes shared with other animal swimmers, whose structural and neurological complexity can obscure these interactions. In comparison with other animal models, the structural simplicity, comparative energetic efficiency, and ease of use in laboratory experimentation allow jellyfish to serve as favorable test subjects for exploration of the hydrodynamic bases of animal propulsion. These same attributes also make jellyfish valuable models for insight into biomimetic or bioinspired engineeringof swimming vehicles. Here, we review advances in understanding of propulsive mechanics derived from jellyfish models as a pathway toward the application of animal mechanics to vehicle designs.

The Hydrodynamics of Jellyfish Swimming

In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos compared to Monte Carlo simulations. It is shown that the generalized polynomial chaos can be orders of magnitude more efficient than Monte Carlo simulations when the dimensionality of random input is low, e.g. for correlated noise.

Performance evaluation of generalized polynomial chaos

An inflation-deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle that serves as the inlet and outlet of water. The fluid-structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices, which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which cause symmetry breaking in the wake. A higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.

Pulsed-jet propulsion of a squid-inspired swimmer at high Reynolds number

Jellyfish - majestic, energy efficient, and one of the oldest species that inhabits the oceans. It is perhaps the second item, their efficiency, that has captivated scientists for decades into investigating their locomotive behavior. Yet, no one has specifically explored the role that their tentacles and oral arms may have on their potential swimming performance, arguably the very features that give jellyfish their beauty while instilling fear into their prey (and beach-goers). We perform comparative in silico experiments to study how tentacle/oral arm number, length, placement, and density affect forward swimming speeds, cost of transport, and fluid mixing. An open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of an idealized flexible jellyfish bell with poroelastic tentacles/oral arms in a viscous, incompressible fluid. Overall tentacles/oral arms inhibit forward swimming speeds, by appearing to suppress vortex formation. Non-linear relationships between length and fluid scale (Reynolds Number) as well as tentacle/oral arm number, density, and placement are observed, illustrating that small changes in morphology could result in significant decreases in swimming speeds, in some cases by downwards of 400% between cases with to without tentacles/oral arms.

Naut your everyday jellyfish model: Exploring how tentacles and oral arms impact locomotion

Jellyfish are majestic, energy-efficient, and one of the oldest species that inhabit the oceans. It is perhaps the second item, their efficiency, that has captivated scientists for decades into investigating their locomotive behavior. Yet, no one has specifically explored the role that their tentacles and oral arms may have on their potential swimming performance. We perform comparative in silico experiments to study how tentacle/oral arm number, length, placement, and density affect forward swimming speeds, cost of transport, and fluid mixing. An open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid–structure interaction problem of an idealized flexible jellyfish bell with poroelastic tentacles/oral arms in a viscous, incompressible fluid. Overall tentacles/oral arms inhibit forward swimming speeds, by appearing to suppress vortex formation. Nonlinear relationships between length and fluid scale (Reynolds Number) as well as tentacle/oral arm number, density, and placement are observed, illustrating that small changes in morphology could result in significant decreases in swimming speeds, in some cases by upwards of 80–90% between cases with or without tentacles/oral arms.

Naut Your Everyday Jellyfish Model: Exploring How Tentacles and Oral Arms Impact Locomotion

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 morphological, muscular, and material properties. We investigated jellyfish locomotion by conducting \textit{in silico} comparative studies and explored swimming performance across different fluid scales (e.g., Reynolds Number), bell contraction frequencies, and contraction phase kinematics 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 (\textit{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 contraction phase kinematics, via Sobol sensitivity analysis, on a high 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.

Don't be jelly: Exploring effective jellyfish locomotion

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.

Jason G. Miles

Papers

Naut Your Everyday Jellyfish Model: Exploring How Tentacles and Oral Arms Impact Locomotion

Naut your everyday jellyfish model: Exploring how tentacles and oral arms impact locomotion

Don't be jelly: Exploring effective jellyfish locomotion

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