Session HJ: Bio-Fluids: Undulatory Flapping II

Toward a three-dimensional viscous vortex particle method for numerical investigations of bio-inspired locomotion

Biological mechanics of aerial and aquatic locomotion are characterized by the reaction force generated by the fluid against highly deforming structures and the resultant vortical wake produced by this interaction. These two features should be central to a high-fidelity computational tool devoted to exploration of bio-inspired mechanics. Motivated by such problems, we present the development of a viscous vortex particle method with coupled body dynamics. The previously developed and validated tool for two-dimensional problems is briefly reviewed. The interaction between vorticity generation, reaction force, and body dynamics, which constitutes the fluid-structure coupling in the method, is discussed, and the capabilities of the method are demonstrated on the passive propulsion of a fish-like system in the wake of an obstacle. The method is extended to three-dimensional problems, and the various components of the solver are highlighted. The core routines of the three-dimensional tool make use of the Parallel Particle-Mesh library, developed by Koumoutsakos and co-workers (J. Comput. Phys., 215, 2006). The new method is demonstrated with preliminary results of a simple model for a dolphin tail with flexible flukes.   

Fully resolved simulation of self-propulsion of aquatic organisms

We present a computational approach for fully resolved simulation of self-propulsion of organisms through a fluid. Our implicit algorithm solves for the translational and rotational motion of the organism for prescribed deformation kinematics. In addition, the solution for the surrounding flow field is also obtained. The approach is easy to apply to the body forms of a variety of organisms. Our final goal is to use this computational tool to help in understanding the mechanisms of movement and its control in aquatic animals. In this abstract we present validation of this method for different organisms. To validate the method with respect to analytical solutions, we consider two cases: 1) a flagellum which propagates plane waves, and 2) a flagellum that propagates helical waves. To validate the method with respect to empirical measurements we consider data from two organisms: 1) jellyfish (data from John Dabiri at Caltech), and 2) zebrafish (data from Melina Hale at The University of Chicago).   

Measuring the material properties of low Reynolds undulatory swimmers

\textit{C. elegans} is a small ($\sim $ 1mm long), free-living nematode that is extensively used as a model organism for biological research, including genomics, cell biology, and neuroscience. In this talk, the swimming behavior of \textit{C. elegans} is investigated both in experiments and in theory. Experiments focus on measuring the nematode swimming behavior (i.e. curvature, frequency, amplitude, etc) in small channels using high-speed imaging microscopy. The swimming kinematics is described using a simple model based on force and moment balances, where the animal is assumed to be modeled as an elastic slender filament immersed in a viscous fluid. We find that this simple model is able to capture the main features of the nematode swimming behavior. Further, we are able to quantify the material properties of the nematode tissue such as elastic and shear moduli by combining detailed experimental kinematics with the analytical model.   

Flexibility and Direction Reversal in Flapping Locomotion

In order to better understand the role of flexibility in the flapping of wings and fins in Nature, experimentalists at NYU have studied a heaving foil with passive pitching. We analyze this system numerically, having constructed a high-order accurate numerical scheme to solve the full Navier-Stokes equations in two-dimensions to study the dynamics. We are able to reproduce qualitatively the results of the experiments: by increasing the flapping frequency, we find regions of improved performance when compared to a rigid wing, regions of under-performance, and a bi-stable regime where the flapping wing can move horizontally in either direction. The numerical simulations have led to predictions of other modes of flapping locomotion, which have subsequently been observed in experiments. We also find that a symmetry breaking transition to forward flapping flight, as observed in experiments of a heaving foil with no pitching, may be directed with only very slight flexibility.   

A vortex shedding model of a flapping membrane

The behavior of a two-dimensional flexible membrane in an imposed axial high-Re flow is investigated. The coupling of the internal solid dynamics and the fluid dynamics makes the direct numerical simulation of this situation a computationally expensive and challenging problem. A reduced-order representation of the flow around the solid is used here to study the coupled dynamics. The vortical wake is accounted for by the shedding of point vortices with monotonically-varying intensity (Brown--Michael vortices) from the trailing edge. This model is used to investigate the flapping flag instability that arises from the competition of the destabilizing pressure difference created by the flag deflection, its bending rigidity and its inertia. The stability of the flag state of rest and the structure of the flapping modes are studied and compared to the results of the linear stability analysis. Finally, a study of the kinematic and dynamic waves traveling along the flag in the flapping regime is presented.   

Performance of skeleton-reinforced biomembranes in locomotion

Skeleton-reinforced biomembranes are ubiquitous in nature and play critical roles in many biological functions. Representative examples include insect wings, cell membranes, and mollusk nacres. In this study we focus on the ray fins of fish and investigate the effects of anisotropic flexibility on their performance. Employing a fluid-structure interaction algorithm by coupling a boundary-element model with a nonlinear structural model, we examined the dynamics of a membrane that is geometrically and structurally similar to a caudal fin. Several locomotion modes that closely resemble caudal fin kinematics reported in the literature are applied. Our results show that the flexibility of the fin significantly increases its capacity of thrust generation, manifested as increased efficiency, reduced transverse force, and reduced sensitivity to kinematic parameters. This design also makes the fin more controllable and deployable. Despite simplifications made in this model in terms of fin geometry, internal structure, and kinematics, detailed features of the simulated flow field are consistent with observations and speculations based upon Particle Image Velocimetry (PIV) measurements of flow around live fish.   

Conflicts between sensory performance and locomotion in weakly electric fish

The knifefish {\em Apteronotus albifrons} hunts for small water insects at night using a self-generated electric field to perceive its world. Using this unique sensory adaptation, the fish senses prey that are near its body with a detection volume that approximates a cylinder that has a length ten times its radius, similar to the fish's elongated body plan. If the fish swims straight, then the back portion of the actively generated detection volume is scanning fluid already scanned by the front portion, but the energy expended to overcome drag is minimized. If it swims with the body pitched, then the rate of volume scanned for prey is increased, but the energy needed to overcome body drag is also increased. In this work we examine the compromise the fish makes between minimizing energy in overcoming drag and maximizing scan rate. We use computational fluid dynamics simulations to assess the impact of changes in body pitch angle on drag, and computational neuroscience simulations to assess the shape and size of the prey detection volume and how body angle changes the scan volume rate.