Fluid dynamics of swimming organisms

Wednesday, June 16 at 05:45pm (PDT)
Thursday, June 17 at 01:45am (BST)
Thursday, June 17 09:45am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS15" time block.
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Laura Miller (University of Arizona, U.S.A.), Arvind Santhanakrishnan (Oklahoma State University, U.S.A.)


The fluid dynamics of animal swimming has been a topic that has interested biologists, mathematicians, physicists, engineers, and artists for hundreds of years. Within the past 20 years, mathematical and numerical methods have been developed to reveal the complexity of how organisms propel themselves through the water. More recent work has revealed how interacting propulsive appendages and organisms can enhance swimming performance. For example, wing-wing interactions, fin-fin interactions, and body-fin interaction can generate additional thrust, enhance lift, and improve maneuverability. In this minisymposium, we use mathematical, physical, and numerical models to better understand the fluid dynamic interactions present in schools of fish, lattices of flapping plates, and the movement of swimming appendages arranged in series. Some of the mathematical challenges involved in studying these problems include the simultaneous resolution of flow between swimming appendages, around the entire organism, and between multiple organisms. The study of animal swimming can provide insight into open questions related to animal behavior, functional morphology, and the bio-inspired design of autonomous underwater vehicles.

Silas Alben

(University of Michigan, U.S.A.)
"Collective locomotion of two-dimensional lattices of flapping plates"
We study the propulsive properties of rectangular and rhombic lattices of flapping plates at O(10--100) Reynolds numbers in incompressible flow. We vary five parameters: flapping amplitude, frequency (or Reynolds number), horizontal and vertical spacings between plates, and oncoming fluid stream velocity. Lattices that are closely spaced in the streamwise direction produce intense vortex dipoles between adjacent plates. The lattices transition sharply from drag- to thrust-producing as these dipoles switch from upstream to downstream orientations at critical flow speeds. The flows assume a variety of periodic and nonperiodic states, with and without up-down symmetry, and multiple stable self-propelled speeds can occur. With small lateral spacing, rectangular lattices yield net drag, while rhombic lattices may generate net thrust efficiently. As lateral spacing increases, rectangular lattices eventually achieve higher efficiencies than rhombic lattices, and the two types of lattice flows converge. At Re = 70, the maximum Froude efficiencies of time-periodic lattice flows are about twice those of an isolated plate. At lower Re, the lattices' efficiency advantage increases until the isolated flapping plate no longer generates thrust.

Anand Oza

(Department of Mathematical Sciences, New Jersey Institute of Technology, U.S.A)
"Coarse-grained models for schooling swimmers"
The beautiful displays exhibited by fish schools and bird flocks have long fascinated scientists, but the role of their complex behavior remains largely unknown. In particular, the influence of hydrodynamic interactions on schooling and flocking has been the subject of intense debate in the scientific literature. I will present a model for flapping wings in orderly formations, with the goal of identifying the formations for which swimmers optimally benefit from hydrodynamic interactions. I will then outline a framework for finding exact solutions to the evolution equations and for assessing their stability, giving physical insight into the preference for certain observed 'schooling states.' The model predictions agree well with experimental data on freely-translating, flapping wings in a water tank. The model is then used to develop a one-dimensional continuum theory for a dense flock, which exhibits traveling wave solutions. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts.

Arvind Santhanakrishnan

(Oklahoma State University, U.S.A.)
"Hydrodynamics of multi-appendage metachronal swimming"
A large number of aquatic invertebrates use metachronal paddling for locomotion, where multiple appendages are oscillated sequentially starting from the back to the front of an animal. The broad diversity of body and appendage morphologies of metachronal swimmers make it difficult to generalize how specific morphological and kinematic parameters impact swimming performance. Modeling approaches can be particularly useful in this context to synthesize physical design principles underlying this successful locomotion strategy. We summarize our studies using robotic models to address how appendage spacing and stroke kinematics affect metachronal swimming performance. We will also present the development of a simplified mathematical model approximating the swimming appendages as pairs of two-dimensional hinged oscillating plates following simple harmonic trajectories. The model accounts for forces on the paddles and on the body to predict the general planar motion in the sagittal plane. Propulsive forces on each paddling appendage are calculated using drag-coefficient models. A comparison of the swimming speed predicted by the model to that of a robotic model will be presented.

Alexander Hoover

(The University of Akron, U.S.A.)
"Emergent metachronal asymmetries in a tension-driven, fluid-structure interaction model of tomopterid parapodia"
Metachronal waves are ubiquitous in propulsive and fluid transport systems across many different scales and morphologies in the biological world. Tomopterids are a soft-bodied, holopelagic polychaete that use metachrony with their flexible, gelatinous parapodia to deftly navigate the midwater ocean column that they inhabit. In the following study, we develop a three-dimensional, fluid-structure interaction model of a tomopterid parapodium to explore the emergent metachronal waves formed from the interplay of passive body elasticity, active muscular tension, and hydrodynamic forces. After introducing our model, we examine the effects that varying material properties have on the stroke of an individual parapodium. We then explore the temporal dynamics when multiple parapodia are placed sequentially and how differences in the phase can alter the collective kinematics and resulting flow field.

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