Session LA: Biofluid Dynamics XII: Swimming-2

Investigation of gliding flight by flying fish

The most successful flight capability of fish is observed in the flying fish. Furthermore, despite the difference between two medium (air and water), the flying fish is well evolved to have an excellent gliding performance as well as fast swimming capability. In this study, flying fish's morphological adaptation to gliding flight is experimentally investigated using dry-mounted darkedged-wing flying fish, $Cypselurus~Hiraii$. Specifically, we examine the effects of the pectoral and pelvic fins on the aerodynamic performance considering (i) both pectoral and pelvic fins, (ii) pectoral fins only, and (iii) body only with both fins folded. Varying the attack angle, we measure the lift, drag and pitching moment at the free-stream velocity of 12m/s for each case. Case (i) has higher lift-to-drag ratio (i.e. longer gliding distance) and more enhanced longitudinal static stability than case (ii). However, the lift coefficient is smaller for case (i) than for case (ii), indicating that the pelvic fins are not so beneficial for wing loading. The gliding performance of flying fish is compared with those of other fliers and is found to be similar to those of insects such as the butterfly and fruitfly.   

Experimental and computational results of harmonically oscillating flexible and rigid flat plates

Oscillating flexible and rigid flat plates are studied with a combination of numerical simulations and experimental measurements. Visualization data and numerical simulations are used to classify the principal characteristics in the wake of the plates. Visualization data for each plate shows distinct differences between when and how efficiently thrust is produced. Visualization results show that thrust is produced at Strouhal numbers of 0.14 for the rigid plate and 0.20 for the flexible plate. Thrust is deemed to be present with the formation of a reverse Karman street. The flow was computed using a high-order compact finite-differences incompressible two-dimensional Navier-Stokes flow solver using an immersed boundary method. This represents a considerable improvement over existing second-order accurate immersed boundary methods. The experimental results are in good agreement with computations when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortex formation.   

Distribution of self-propelled organisms in fluid flows

We study the distribution of microorganisms represented as self-propelled particles in a moving fluid medium. The particles are advected by the flow and, in addition, they swim in a direction controlled by external factors. Two cases are considered: 1. passive spheroidal particles, that swim with constant speed but the swimming direction is reoriented by the viscous torque acting on the spheroid due to the local velocity field, and 2. chemotactic particles, whose swimming speed is oriented and proportional to the gradient of the concentration of a chemoattractant. We show that the combined effects of chaotic mixing and chemotaxis or flow reorientation leads to aggregation of the particles along a complex manifold. We analyse the properties of the aggregates and the efficiency of chemotaxis in flows with strongly non-uniform fluctuating distribution of the chemottractant.   

Simulation of suspensions of hydrodynamically interacting self-propelled particles

Simulations of large populations of confined hydrodynamically interacting swimming particles are performed at low Reynolds number. Each swimmer is modeled as a bead-rod dumbbell with a propulsion force exerted on one bead (with an equal and opposite force exerted on the fluid) and excluded volume potentials at the beads and center of mass. Hydrodynamic coupling between the swimmers leads to large-scale vortex motions and regimes of anomalous diffusion that are qualitatively consistent with experimental observations. At low concentrations, hydrodynamic interactions cause the swimmers to form pairs while the swimming speed remains unchanged or is slightly reduced from the value for isolated swimmers. In confined geometries, the swimmers migrate towards solid surfaces organizing in layers where the swimmers form larger groups, especially in highly confined (monolayer) geometries. As the concentration is increased, the swimming speed also increases due to large-scale collective motion; in confined geometries the layers at the walls and the larger groups are disrupted.   

Reciprocal motion at low Reynolds numbers

At low Reynolds numbers, the equations of motion are time-reversible. Consequently, if the periodic motion of a solid body is symmetric in time (so called reciprocal motion), the body - on average - will not move. One way to overcome this constraint is to use non-reciprocal motion, as do the flagella of swimming microorganisms. Another way is to allow the body to be flexible. In this talk, we will discuss a third possibility: the reciprocal motion of a solid body can lead to net motion if the surrounding environment is able to deform in response to the motion of the body. We will present simple scalings and a macro-scale experiment to support this idea.   

Recording High Resolution 3D Lagrangian Motions In Marine Dinoflagellates using Digital Holographic Microscopic Cinematography

Detailed data on swimming behavior and locomotion for dense population of dinoflagellates constitutes a key component to understanding cell migration, cell-cell interactions and predator-prey dynamics, all of which affect algae bloom dynamics. Due to the multi-dimensional nature of flagellated cell motions, spatial-temporal Lagrangian measurements of multiple cells in high concentration are very limited. Here we present detailed data on 3D Lagrangian motions for three marine dinoflagellates: \textit{Oxyrrhis marina}, \textit{Karlodinium veneficum}, and \textit{Pfiesteria piscicida}, using digital holographic microscopic cinematography. The measurements are performed in a 5$\times $5$\times $25mm cuvette with cell densities varying from 50,000 $\sim $ 90,000 cells/ml. Approximately 200-500 cells are tracked simultaneously for 12s at 60fps in a sample volume of 1$\times $1$\times $5 mm at a spatial resolution of 0.4$\times $0.4$\times $2 $\mu $m. We fully resolve the longitudinal flagella ($\sim $200nm) along with the Lagrangian trajectory of each organism. Species dependent swimming behavior are identified and categorized quantitatively by velocities, radii of curvature, and rotations of pitch. Statistics on locomotion, temporal {\&} spatial scales, and diffusion rate show substantial differences between species. The scaling between turning radius and cell dimension can be explained by a distributed stokeslet model for a self-propelled body.   

Flow over a Biomimetic Surface Roughness Microgeometry

Certain species of sharks (e.g. shortfin mako and common hammerhead) have a skin structure that could result in a bristling of their denticles (scales) during increased swimming speeds (Bechert, D. W., Bruse, M., Hage, W. and Meyer, R. 2000, Fluid mechanics of biological surfaces and their technological application. Naturwissenschaften 80:157-171). This unique surface geometry results in a three-dimensional array of cavities* (d-type roughness geometry) forming within the surface and has been given the acronym MAKO (Micro-roughness Array for Kinematic Optimization). Possible mechanisms leading to drag reduction over the shark's body by this unique roughness geometry include separation control thereby reducing pressure drag, skin friction reduction (via the `micro-air bearing' effect first proposed by Bushnell (AIAA 83-0227)), as well as possible transition delay in the boundary layer. Initial work is confined to scaling up the geometry from 0.2 mm on the shark skin to 2 cm, with a scaling down in characteristic velocity from 10 - 20 m/s to 10 - 20 cm/s for laminar flow boundary layer water tunnel studies. Support for this research by NSF SGER grant CTS-0630489 and a University of Alabama RAC grant is gratefully acknowledged. * Patent pending.   

Investigation of Scaling Effects on Fish Pectoral Fin Performance

Reynolds and Strouhal numbers are two key parameters that can potentially affect the performance of rigid and deformable flapping foils. Flow past a deformable pectoral fin of a fish in steady forward motion (speed of 1 BL/s) is simulated using a Cartesian grid immersed boundary solver. Investigation of the scaling of the performance with these two parameters allows us to gain better insight into the fundamental mechanisms of the thrust production as well as address the practical question of how the performance of a fin is expected to change with changes in size, speed and frequency. It is found that the essential fluid dynamic mechanisms are unchanged with Reynolds number. We observe that although the vortex structures get more complicated with increasing Re, the key features (like the strong tip vortex, leading and trailing edge vortices) are similar in all the cases. On the other hand, the hydrodynamic performance of the fin is found to be quite sensitive to the Strouhal number. A set of numerical simulations of fin gaits synthesized from the POD modes are also carried out. This approach allows us to connect specific features in the fin gait with the observed vortex dynamics and hydrodynamic force production.   

The Effects of Eddies on Fish Swimming Ability

In order to quantify the effect of turbulent flow perturbations on fish swimming, Creek Chub (\textit{Semotilus atromaculatus}) were swum in low turbulence flume under various eddy fields. The cross-section of the flume where fish are positioned for the tests is 60cm x 60cm. Fish length varied from 10 to 14 cm. Eddies were generated using six arrays of equally spaced cylinders. The cylinder diameter and orientation were varied between arrays to produce eddy fields with differing eddy compositions. The result was a matrix of eddy fields in which the dominant eddies were either smaller, the same size, or larger than the fish length and of either horizontal or vertical orientation. A control was also run using a 1 cm by 1 cm upstream diffuser. An incremental velocity test was conducted in which the speed was increased by 3.6 cm/s every 2 minutes until the fish was exhausted. Simultaneous plan and side view video analysis was conducted producing body oscillation and fin utilization statistics. Using particle image velocimetry, it was determined that eddy size, circulation, and orientation impact the critical swimming speed and fin utilization of creek chub. The tests were designed such that the results may be built upon to guide design of more complicated restoration and fish passage projects.   

Hydrodynamic Performance of a Flexible Fish Pectoral Fin

Numerical simulations have been used to examine in detail the hydrodynamic performance of a pectoral fin of a bluegill sunfish. The pectoral fin of this fish is highly flexible and undergoes significant shape and area change during its flapping cycle. The numerical simulations employ a 3D immersed boundary solver that allows us to examine in detail the hydrodynamics of the fin. Simulations reveal that the fish uses the fin flexibility to produce a highly complex and asymmetric stroke that does not fit any of the classic notions of ``paddling'' or ``flapping.'' The numerical simulations clearly reveal the distinct vortex structured produced by the fin and the connection between the vortex structures and hydrodynamic performance is examined. Finally, comparison between a flexible fish fin and a rigid flapping foil allows us to assess the benefits of flexibility on the hydrodynamic performance.   

Dynamics of \textit{C. elegans} in various fluidic environments

\textit{C. elegans} is a freely moving soil nematode that crawls or swims by propagating a body wave backwards. In fluids we investigate its swimming locomotion as the fluid viscosity is varied over many orders of magnitude and in the presence of non-Newtonian fluid responses. For Newtonian fluids we find power-law relations between swimming speed and fluid viscosity, and these relations are not in accordance with assumptions of constant power input to the fluid. We also find that the Strouhal frequency is nearly independent of viscosity and swimming speed. We investigate the influence of confinement on \textit{C. elegans} locomotion and find that interactions between confining walls and body undulations can markedly increase swimming speed.   

PIV Measurements of Tethered and Free-swimming Copepodid Flow Fields

Accurately visualizing and quantifying the flow field created by copepod movement is important for understanding ecological processes such as feeding and hydrodynamic signal detection. Copepods used in studies addressing these issues are often tethered at a fixed location to simplify experiments and reduce data collection time. In this study, we compared the flow field generated by tethered and free-swimming \textit{Euchaeta antarctica} using the particle image velocimetry (PIV) technique. The tethered copepodid flow field contained asymmetrical regions of high velocity, higher maximum velocities, and a greater rate of kinetic energy dissipation compared to the free-swimming copepodid flow field. The differences in the flow field are explained by considering the forces on the free swimming specimen compared to the tethered specimen. Viscous flow theory demonstrates that the force on the fluid due to the presence of the tether irrevocably modifies the flow field in a manner that is consistent with the measurements. Due to the differences in the flow field, calculations of biological quantities, such as energetic costs, filtering rates, and the volume of fluid influenced by zooplankton, differ for tethered versus free-swimming (natural) conditions.