Dynamic boundaries in flowing fluids, from erosion sculptures to flapping wing flight

Textbook fluid mechanics addresses steady flows past fixed, rigid objects. However, Nature rarely obeys such restrictions and instead offers many fascinating situations involving the mutual influence of dynamic structures and unsteady flows. Such problems are complex because changes in shape affect flow, which in turn alters shape, and so on. Drawing inspiration from biological and geophysical flows, our Applied Math Lab attacks such fluid–structure interaction problems through tabletop experiments, math modeling, and computational simulations. I will present several case studies from the slow but persistent sculpting of erodible boundaries by flowing fluids to the fast flapping wing motions of insects and their robotic cousins

Lattices of hydrodynamically interacting flapping swimmers

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory

Metallic microswimmers driven up the wall by gravity

Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show that tail-heavy swimmers preferentially orient upwards and ascend along inclined planes. We show that such gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even ultraheavy microswimmers to climb nearly vertical surfaces. Theory and simulations show that the buoyancy or gravitational torque that tends to align the rods is reinforced by a fore-aft drag asymmetry induced by hydrodynamic interactions with the wall.MRSEC Program of the National Science Foundation under Award DMR-1420073 NSF Grants DMS-RTG-1646339, DMS-1463962 and DMS-1620331. Tamkeen under the NYU Abu Dhabi Research Institute grant CG002 “la Caixa” Foundation (ID 100010434) fellowship LCF/BQ/PI20/11760014 European Union’s Horizon 2020 under the Marie Sklodowska-Curie grant agreement No 847648

Dynamic self-assembly of microscale rotors and swimmers.

Biological systems often involve the self-assembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a well-controlled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components self-assemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micron-scale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial run-and-tumble motion

Dynamics, Control, And Stability Of Fruit Fly Flight

The flight of insects is a beautiful example of an organism's complex interaction with its physical environment. Consider, for example, a fly's evasive dodge of an approaching swatter. The insect must orchestrate a cascade of events that starts with the visual system perceiving information that is then processed and transmitted through neural circuits. Next, muscle actions are triggered that induce changes to the insect's wing motions, and these motions interact with fluid flows to generate aerodynamic forces. Though not as obvious to appreciate, simply flying straight and keeping upright require similarly complex events in order to overcome unexpected disturbances and suppress intrinsic instabilities. Here, I present recent progress in dissecting the many layers that comprise maneuvering and stabilization in the flight of the fruit fly, D. melanogaster. My emphasis is on aspects of flight at the interface of biology and physics, and I seek to understand how physical effects both constrain and simplify biological strategies. This body of work roughly divides into three thrusts: the development of experimental and modeling methods, studies of actuation and control of maneuvering flight, and studies of control during flight stabilization. In Chapter 2, I discuss the experimental techniques we have developed for gathering many three-dimensional high-speed videos of insect flight. In addition, I outline our approach for automated extraction of body and wing motions from such videos. In Chapter 3, I show how experimental observations can be combined with aero- dynamic models to reveal that fruit flies use paddling motions to drive forward flight. In Chapter 4, I review our work on turning maneuvers with an emphasis on how the wing motions themselves arise through an actuation mechanism. In Chapter 5, I outline a set of experimental and modeling techniques for understanding how insects recover from in-flight perturbations to their heading. In Chapter 6, I use a similar approach to analyze the intrinsic instability of body pitch and predict the reaction time needed to stabilize flight. In Chapter 7, I include work on the hydrodynamic interactions between flapping bodies in a fluid flow