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Swimming performance, resonance and shape evolution in heaving flexible panels
- Alexander P. Hoover, Ricardo Cortez, Eric D. Tytell, Lisa J. Fauci
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- Journal:
- Journal of Fluid Mechanics / Volume 847 / 25 July 2018
- Published online by Cambridge University Press:
- 23 May 2018, pp. 386-416
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Many animals that swim or fly use their body to accelerate the fluid around them, transferring momentum from their flexible bodies and appendages to the surrounding fluid. The kinematics that emerge from this transfer result from the coupling between the fluid and the active and passive material properties of the flexible body or appendages. To elucidate the fundamental features of the elastohydrodynamics of flexible appendages, recent physical experiments have quantified the propulsive performance of flexible panels that are actuated on their leading edge. Here we present a complementary computational study of a three-dimensional flexible panel that is heaved sinusoidally at its leading edge in an incompressible, viscous fluid. These high-fidelity numerical simulations enable us to examine how propulsive performance depends on mechanical resonance, fluid forces, and the emergent panel deformations. Moreover, the computational model does not require the tethering of the panel. We therefore compare the thrust production of tethered panels to the forward swimming speed of the same panels that can move forward freely. Varying both the passive material properties and the heaving frequency of the panel, we find that local peaks in trailing edge amplitude and forward swimming speed coincide and that they are determined by a non-dimensional quantity, the effective flexibility, that arises naturally in the Euler–Bernoulli beam equation. Modal decompositions of panel deflections reveal that the amplitude of each mode is related to the effective flexibility. Panels of different material properties that are actuated so that their effective flexibilities are closely matched have modal contributions that evolve similarly over the phase of the heaving cycle, leading to similar vortex structures in their wakes and comparable thrust forces and swimming speeds. Moreover, local peaks in the swimming speed and trailing edge amplitude correspond to peaks in the contributions of the different modes. This computational study of freely swimming flexible panels gives further insight into the role of resonance in swimming performance that is important in the engineering and design of robotic propulsors. Moreover, we view this reduced model and its comparison to laboratory experiments as a building block and validation for a more comprehensive three-dimensional computational model of an undulatory swimmer that will couple neural activation, muscle mechanics and body elasticity with the surrounding viscous, incompressible fluid.
Nutrient transport and acquisition by diatom chains in a moving fluid
- MAGDALENA M. MUSIELAK, LEE KARP-BOSS, PETER A. JUMARS, LISA J. FAUCI
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- Journal:
- Journal of Fluid Mechanics / Volume 638 / 10 November 2009
- Published online by Cambridge University Press:
- 18 September 2009, pp. 401-421
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The role of fluid motion in delivery of nutrients to phytoplankton cells is a fundamental question in biological and chemical oceanography. In the study of mass transfer to phytoplankton, diatoms are of particular interest. They are non-motile, are often the most abundant components in aggregates and often form chains, so they are the ones expected to benefit most from enhancement of nutrient flux due to dissipating turbulence. Experimental data to test the contribution of advection to nutrient acquisition by phytoplankton are scarce, mainly because of the inability to visualize, record and thus imitate fluid motions in the vicinities of cells in natural flows. Laboratory experiments have most often used steady Couette flows to simulate the effects of turbulence on plankton. However, steady flow, producing spatially uniform shear, fails to capture the diffusion of momentum and vorticity, the essence of turbulence. Thus, numerical modelling plays an important role in the study of effects of fluid motion on diffusive and advective nutrient fluxes. In this paper we use the immersed boundary method to model the interaction of rigid and flexible diatom chains with the surrounding fluid and nutrients. We examine this interaction in two nutrient regimes, a uniform background concentration of nutrients, such as might be typical of an early spring bloom, and a contrasting scenario in which nutrients are supplied as small, randomly distributed pulses, as is more likely for oligotrophic seas and summer conditions in coastal and boreal seas. We also vary the length and flexibility of chains, as whether chains are straight or bent, rigid or flexible will affect their behaviour in the flow and hence their nutrient fluxes. The results of numerical experiments suggest that stiff chains consume more nutrients than solitary cells. Stiff chains also experience larger nutrient fluxes compared to flexible chains, and the nutrient uptake per cell increases with increasing stiffness of the chain, suggesting a major advantage of silica frustules in diatoms.
A computational model of the collective fluid dynamics of motile micro-organisms
- MATTHEW M. HOPKINS, LISA J. FAUCI
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- Journal:
- Journal of Fluid Mechanics / Volume 455 / 25 March 2002
- Published online by Cambridge University Press:
- 15 April 2002, pp. 149-174
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A mathematical model and numerical method for studying the collective dynamics of geotactic, gyrotactic and chemotactic micro-organisms immersed in a viscous fluid is presented. The Navier–Stokes equations of fluid dynamics are solved in the presence of a discrete collection of micro-organisms. These microbes act as point sources of gravitational force in the fluid equations, and thus affect the fluid flow. Physical factors, e.g. vorticity and gravity, as well as sensory factors affect swimming speed and direction. In the case of chemotactic microbes, the swimming orientation is a function of a molecular field. In the model considered here, the molecules are a nutrient whose consumption results in an upward gradient of concentration that drives its downward diffusion. The resultant upward chemotactically induced accumulation of cells results in (Rayleigh–Taylor) instability and eventually in steady or chaotic convection that transports molecules and affects the translocation of organisms. Computational results that examine the long-time behaviour of the full nonlinear system are presented.
The actual dynamical system consisting of fluid and suspended swimming organisms is obviously three-dimensional, as are the basic modelling equations. While the computations presented in this paper are two-dimensional, they provide results that match remarkably well the spatial patterns and long-time temporal dynamics of actual experiments; various physically applicable assumptions yield steady states, chaotic states, and bottom-standing plumes. The simplified representation of microbes as point particles allows the variation of input parameters and modelling details, while performing calculations with very large numbers of particles (≈104–105), enough so that realistic cell concentrations and macroscopic fluid effects can be modelled with one particle representing one microbe, rather than some collection of microbes. It is demonstrated that this modelling framework can be used to test hypotheses concerning the coupled effects of microbial behaviour, fluid dynamics and molecular mixing. Thus, not only are insights provided into the differing dynamics concerning purely geotactic and gyrotactic microbes, the dynamics of competing strategies for chemotaxis, but it is demonstrated that relatively economical explorations in two dimensions can deliver striking insights and distinguish among hypotheses.