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The hydrodynamics of swimming at the millimeter-to-centimeter scale often present the challenge of having both viscous and inertial effects playing nontrivial roles. Inertial forces arise from the momentum of a moving fluid, while viscous forces come from friction within the flow. The non-dimensional Reynolds number (Re) compares the magnitudes of the inertial and viscous forces within a flow. At low Re (≪ 1), viscous forces dominate; at higher Re (≫ 1), inertial forces are more important. Efforts to understand the hydrodynamics of swimming have mainly focused on the extremes of fully viscous-dominated (Re ≪ 1) or inertia-dominated flow (Re ≫ 1). However, many animals swim in an intermediate regime, where inertia and viscosity are both significant. As an impactful and generalizable case study, we focus on ctenophores (comb jellies), a type of marine zooplankton. Ctenophores swim via the coordinated rowing of numerous highly flexible appendages (ctenes), with Reynolds numbers on the order of 10-100. Their locomotory dynamics present a unique opportunity to study the scaling of rowing (drag-based propulsion) across the low to intermediate Reynolds number range. With a combination of animal experiments, reduced-order analytical modeling, and physical-robotic modeling, we investigate how the kinematic and geometric variables of beating ctenes vary across Re, and how they affect swimming (including force production, speed, and maneuverability). Using animal experiments, we quantify the spatiotemporal asymmetry of beating ctenes across a wide range of animal sizes and Re. With our reduced-order model—the first to incorporate adequate formulations for the viscous-inertial nature of this regime—we explore the maneuverability and agility displayed by ctenophores, and show that by controlling the kinematics of their distributed appendages, ctenophores are capable of nearly omnidirectional swimming. Finally, we use a compliant robotic model that mimics ctenophore rowing kinematics to study rowing performance with direct calculation of thrust and lift forces distributed along the propulsor. These experiments shed new light on the relationship between motion asymmetries and thrust and lift production. This combination of animal experiments, analytical modeling, and physical modeling is the most detailed study of low to intermediate Re rowing to date, and provides a foundation for future applications in bio-inspired design.
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Reciprocal swimming at intermediate Reynolds number
In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers $${\textit Re} \approx 1$$ –1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate $${\textit {Re}}$$ . In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.
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- Award ID(s):
- 1753148
- PAR ID:
- 10412701
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 952
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.873
