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The papers listed below (with abstract) are either already published or in the state been written or been submitted. A few more new works are still on the production line. They are: (1) the urban heat island effect due to air conditioning; (2) mobile heat blanket on thermal convection with annular geometry; and etc.


ratcheting fluids using geometric anisotropy,
file coming soon
B. Thiria and J. Zhang
Submitted
(2013)


persistent heat islands induced by air conditioning,
file coming soon
B. Liu and J. Zhang
submitted
(2013)

Abstract: Coming soon.


hydrodynamic capture of microswimmers into sphere-bound orbits,
click to review pdf
D. Takagi, J. Palacci, A. Braunschweig, M. Shelley and J. Zhang
Soft Matter 10, 1784
(2014)

Abstract:
Self-propelled particles can exhibit surprising non-equilibrium behaviors, and how they interact with obstacles or boundaries remains an important open problem. Here we show that chemically propelled micro-rods can be captured, with little change in their speed, into close orbits around solid spheres resting on or near a horizontal plane. We show that this interaction between sphere and particle is short-range, occurring even for spheres smaller than the particle length, and for a variety of sphere materials. We consider a simple model, based on lubrication theory, of a force- and torque-free swimmer driven by a surface slip (the phoretic propulsion mechanism) and moving near a solid surface. The model demonstrates capture, or movement towards the surface, and yields speeds independent of distance. This study reveals the crucial aspects of activity-driven interactions of self-propelled particles with passive objects, and brings into question the use of colloidal tracers as probes of active matter.


self-similar evolution of a body eroding in a fluid flow,
click to review pdf
M. Moore, L. Ristroph, S. Childress, J. Zhang, and M. Shelley
Phys. of Fluids 25, 116602
(2013)

Abstract:
Erosion of solid material by flowing fluids plays an important role in shaping landforms, and in this natural context is often dictated by processes of high complexity. Here, we examine the coupled evolution of solid shape and fluid flow within the idealized setting of a cylindrical body held against a fast, unidirectional flow, and eroding under the action of fluid shear stress. Experiments and simulations both show self-similar evolution of the body, with an emerging quasi-triangular geometry that is an attractor of the shape dynamics. Our fluid erosion model, based on Prandtl boundary layer theory, yields a scaling law that accurately predicts the body's vanishing rate. Further, a class of exact solutions provides a partial prediction for the body's terminal form as one with a leading surface of uniform shear stress. Our simulations show this predicted geometry to emerge robustly from a range of different initial conditions, and allow us to explore its local stability. The sharp, faceted features of the terminal geometry defy the intuition of erosion as a globally smoothing process.


dispersion of self-propelled rods undergoing fluctuation-driven flips,
click to review pdf
D. Takagi, A. Braunschweig, J. Zhang, and M. Shelley
Phys. Rev. Lett. 110, 038301
(2013)

Abstract:
Synthetic microswimmers may someday perform medical and technological tasks, but predicting their motion and dispersion is challenging. Here we show that chemically propelled rods tend to move on a surface along large circles but curiously show stochastic changes in the sign of the orbit curvature. By accounting for fluctuation-driven flipping of slightly curved rods, we obtain analytical predictions for the ensemble behavior in good agreement with our experiments. This shows that minor defects in swimmer shape can yield major long-term effects on macroscopic dispersion.


fluid-structure interactions: research in the courant institute's applied mathematics laboratory,
click to review pdf
S. Childress, M. Shelley, and J. Zhang
Comm. on Pure and Applied Math. 65, 1697
(2012)

Abstract:
The Applied Mathematics Laboratory is a research laboratory within the Mathematics Department of the Courant Institute. It was established to carry out physical experiments, modeling, and associated numerical studies in a variety of problems of interest to Courant faculty, postdocs, and graduate and undergraduate students. Most of the research to date has involved fluid mechanics, and we focus in this paper on the work that relates to the interaction of fluids with rigid, movable, or flexible bodies.


sculpting of an erodible body by flowing water,
click to review pdf
L. Ristroph, N. Moore, S. Childress, M. Shelley, and J. Zhang
PNAS 109, 19606
(2012)

Abstract:
Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process,wefind that erosion sculpts pointed and cornerlike features that persist as the solid shrinks.Weexplain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to selfsimilarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature.


wireless powering of ionic polymer metal composites toward howering microswimmers,
click to review pdf
K. Abdelnour, A. Stinchcombe, M. Porfiri, J. Zhang, and S. Childress
IEEE-ASME Transactions on Mechatronics, 17, 924
(2012)

Abstract:
In this paper, we present the design of a wireless powering system for ionic polymer metal composites (IPMCs). The system design is motivated by the need for enabling technologies to replicate hovering flight and swimming in biological systems. IPMC wireless powering is achieved by using radio frequency magnetically coupled coils and in-house designed power electronics for low-frequency IPMC actuation. Parameters of the circuit components describing the resonantly coupled coils and the IPMC are experimentally identified. The power transfer from the external power source to the receiver at the IPMC is experimentally analyzed for a broad range of system parameters. Flow visualization and particle image velocimetry are used to ascertain the system capabilities. Moreover, the IPMC vibration in the wireless and wired configurations is compared.


experiments and theory of undulatory locomotion in a simple structured medium,
click to review pdf
T. Majmudar, E. Keaveny, J. Zhang, and M. Shelley
J. of Royal Society, Interface, 9, 1809
(2012)

Abstract:
Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics.


oscillations of a layer of viscoelastic fluid under steady forcing,
click to review pdf
Bin Liu, Mike Shelley, and Jun Zhang
J. of non-Newtonian Fluid Mechanics, 175, 38
(2012)

Abstract:
We study the dynamics of a layer of viscoelastic fluid, in the Stokesian regime, that is driven from below by a 4 x 4 checkerboard pattern of rotating and counter-rotating disks. At low disk rotation rate (low Weissenberg number) the fluid flow response is slaved to the geometry of this forcing and divides into many steadily rotating cells, each contained within invariant manifolds issuing from hyperbolic stagnation points. As the rotation rate increases these fluid cells begin to oscillate periodically in a synchronized fashion. At a yet higher rotation rate, this temporally periodic flow disappears and is replaced by a richer, "turbulent" dynamics where the flow is delocalized from the forcing and has fluid cells that are continuously destroyed and reformed.


intrinsic stability of a body hovering in an oscillating airflow,
click to review pdf
Bin Liu, Leif Ristroph, Annie Weathers, Stephen Childress, and Jun Zhang
Physical Review Letters, 108, 068103
(2012)

Abstract:
We explore the stability of flapping flight in a model system that consists of a pyramid-shaped object hovering in a vertically oscillating airflow. Such a flyer not only generates sufficient aerodynamic force to keep aloft but also robustly maintains balance during free flight. Flow visualization reveals that both weight support and orientational stability result from the periodic shedding of vortices. We explain these findings with a model of the flight dynamics, predict increasing stability for higher center of mass, and verify this counterintuitive fact by comparing top- and bottom-heavy flyers.


flapping and bending bodies interacting with fluid flows,
click to review pdf
Michael Shelley and Jun Zhang
Annual Review of Fluid Mechanics, 43, 449-465
(2011)

Abstract:
The flapping or bending of a flexible planar structure in a surrounding fluid flow, which includes the flapping of flags and the self-streamlining of flexible bodies, constitutes a central problem in the field of fluid-body interactions. Here we review recent, highly detailed experiments that reveal new nonlinear phenomena in these systems, as well advances in theoretical understanding, resulting in large part from the rapid development of new simulation methods that fully capture the mutual coupling of fluids and flexible solids


focused force transmission through an aqueous suspension of granules,
click to review pdf
Bin Liu, Michael Shelley and Jun Zhang
Physical Review Letters, 105, 188301
(2010)

Abstract:
We investigate force transmission through a layer of shear-thickening fluid, here a concentrated aqueous cornstarch suspension. When a solid body is pushed through this complex fluid and approaches its containing wall, a hardened volume of the suspension is observed that adds to the leading side of the body. This volume leads to an imprint on the wall which is made of molding clay. By studying the geometry of the hardened volume, inferred by the imprint shapes, we find that its geometry is determined by the size and speed of the body. By characterizing the response of the clay to deformation we show that the force transmitted through the suspension to the wall is localized. We also study other aspects of this dynamical hardening of the suspension, such as the effect of the substrate and body shape, and its relaxation as the imposed straining is stopped.


surprising behaviors in flapping locomotion with passive pitching,
click to review pdf
Saverio E. Spagnolie, Lionel Moret, Michael Shelley and Jun Zhang
Physics of Fluids, 22, 041903
(2010)

Abstract:
To better understand the role of wing and fin flexibility in flapping locomotion, we study through experiment and numerical simulation a freely moving wing that can "pitch" passively as it is actively heaved in a fluid. We observe a range of flapping frequencies corresponding to large horizontal velocities, a regime of underperformance relative to a clamped nonpitching flapping wing, and a surprising, hysteretic regime in which the flapping wing can move horizontally in either direction !despite left/right symmetry being broken by the specific mode of pitching. The horizontal velocity is shown to peak when the flapping frequency is near the immersed system's resonant frequency. Unlike for the clamped wing, we find that locomotion is achieved by vertically flapped symmetric wings with even the slightest pitching flexibility, and the system exhibits a continuous departure from the Stokesian regime. The phase difference between the vertical heaving motion and consequent pitching changes continuously with the flapping frequency, and the direction reversal is found to correspond to a critical phase relationship. Finally, we show a transition from coherent to chaotic motion by increasing the wing's aspect ratio, and then a return to coherence for flapping bodies with circular cross section.


hovering of a rigid pyramid in an oscillatory airflow,
click to review pdf
Annie Weathers, B. Folie, Bin Liu, Stephen Childress and Jun Zhang
Journal of Fluid Mechanics, 650, 415
(2010)

Abstract:
We investigate the dynamics of rigid bodies (hollow 'pyramids') placed within a background airflow, oscillating with zero mean. The asymmetry of the body introduces a net upward force. We find that when the amplitude of the airflow is above a threshold, the net lift exceeds the weight and the object starts to hover. Our results show that the objects hover at far smaller air amplitudes than would be required by a quasi-steady theory, although this theory accounts qualitatively for the behaviour of the system as the body mass becomes small.


flapping flags in tandem,
click to view pdf
Leif Ristroph and Jun Zhang
Physics Today, November, 108
(2008)

Note: This work was selected by Physics Today and published in the section "Back Scatter."


anomalous hydrodynamic drafting of interacting flapping flags,
click to view pdf
Leif Ristroph and Jun Zhang
Physical Review Letters, 101, 194502
(2008)

Abstract:
In aggregates of objects moving through a fluid, bodies downstream of a leader generally experience reduced drag force. This conventional drafting holds for objects of fixed shape, but interactions of deformable bodies in a flow are poorly understood, as in schools of fish. In our experiments on ``schooling" flapping flags we find that it is the leader of a group who enjoys a significant drag reduction (of up to 50 %), while the downstream flag suffers a drag increase. This counterintuitive inverted drag relationship is rationalized by dissecting the mutual influence of shape and flow in determining drag. Inverted drafting has never been observed with rigid bodies, apparently due to the inability to deform in response to the altered flow field of neighbors.

This work was highlighted on the cover of Phys. Rev. Lett. (Nov. 7, 2008), on the backcover of Physics Today's "Back Scatter" (Nov. 2008), in the "Research Highlights" of journal Nature (London, v456, p284, 2008) and in Economist (London, Nov.27).


self-induced cyclic reorganization of many bodies through thermal convection,
click to view pdf
Bin Liu and Jun Zhang
Physical Review Letters, 100, 244501
(2008)

Abstract:
We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of many-body interactions mediated by thermal convection, which gives rise to surprising robust oscillations between di erent large-scale circulations. Once begun, this process repeats cyclically, with the collection of spheres entrained and packed from one side of the convection cell to the other. The frequency of the cycle is highest when the spheres occupy about half of the cell bottom and their size coincides with the thickness of the thermal boundary layer. This phenomenon shows that a deformable mass can stimulate a turbulent, thermally convecting fluid into oscillation, a collective behavior that may be found in nature.

This work was highlighted by Phys. Rev. Focus, New Scientist, and a few other sci-news sources.


an experimental investigation and a simple model of a valveless pump,
click to view pdf
Thomas Bringley*, Stephen Childress, Nicolas Vandenberghe, and Jun Zhang
Physics of Fluids, 20, 033602
(2008)

Abstract:
We construct a valveless pump consisting of a section of elastic tube and a section of rigid tube connected in a closed loop and filled with water. Periodically squeezing the elastic tube at an asymmetric location generates a flow of water around the tubes. This effect, called the Liebau phenomenon or valveless pumping, has been known for some time, but is still poorly understood. We study the flow rates for various squeezing locations, frequencies, and elastic tube rigidities. To understand how valveless pumping works, we formulate a simple model that can be described by coupled ordinary differential equations. The time series of flow velocities generated by the model are qualitatively and quantitatively similar to those seen in the experiment. The model provides a physical explanation of valveless pumping, and it allows us to identify the essential pumping mechanisms.

* In memory of Dr. Tom Bringley (1981-2008), who fought cancer for three years with great courage and dignity. It was our privilege to work with this optimistic, original, strong and very friendly young man.


*flapping dynamics of passive and active structures in moving fluid,
pdf coming soon
Jun Zhang
*to be submitted to Experiments in Fluids (special issue on swimming),
Jan., 2007

Abstract:
Motivated by the swimming and flying locomotion found in the biological world, we perform laboratory experiments aimed to understand the basic thrust-generation mechanism through the flapping of thin structures. We first focus on the passive dynamics of flexible bodies that interact with the surrounding high speed flows. The emerging dynamical states are compared with the swimming modes of fish. We further investigate the self-sustained forward motion of a flat plate -- a prototypical wing or fin -- that is flapped up and down in a fluid. Its forward locomoting speed is sensitively determined by its geometry and flapping frequency. A scaling analysis is proposed to explain such dependences. Moreover, we also explore possible scenarios to increase the forward speed by incorporating wing flexibility, passive pitching and asymmetry in the design of our prototypical wings. The ultimate goal of our investigation is to find the minimum wing design that still ensures efficient thrust generation. Insights gained from this study would help us further appreciate and understand the subtle differences among all the modes and controls used in animal locomotion.

a free boundary interacts with a thermally convecting fluid,
click to view pdf
Jun Zhang and Jin-Qiang Zhong
submitted as an entry for "Gallery of Fluid Motion" to the APS/DFD meeting, nov., (2007)


modeling the dynamics of a free boundary on turbulent thermal convection,
click to view pdf
Jin-Qiang Zhong and Jun Zhang
Physical Review E, 76, 016307
(2007)

Abstract:
Based on our previous experimental study, we present a one-dimensional, phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations.


dynamical states of a mobile heat blanket on a thermally convecting fluid,
click to view pdf
Jin-Qiang Zhong and Jun Zhang
Physical Review E, 75, 055301(R),
(2007)

Abstract:
We study experimentally the dynamical states of a freely-moving, floating heat blanket that couples with a thermally convective fluid. The floating boundary modifies the large-scale flow pattern in the bulk and destabilizes the coupled system, leading to spontaneous oscillations. The system makes a transition from the oscillatory state to a weakly confined state as the moving boundary exceeds a critical size. In the latter state, the moving boundary roams about the center of the convection cell and executes random excursions due to nearby passing thermal plumes. To understand the observed states and the transition, we provide a low-dimensional model that appears to capture the underlying mechanism of the coupled system.


standing surface waves on a semi-toroidal water ring,
click to view pdf
S. Jung, E. Kim, M. Shelley and Jun Zhang
Physics of Fluids, 19, 058105
(2007)

Abstract:
We study the nature of surface waves on a semi-toroidal ring of water. We create this specific fluid shape by patterning a glass plate with a hydrophobic film, which confines the fluid to a precise geometric region. To excite the system, the supporting plate is vibrated up and down, thus accelerating/decelerating the fluid ring along its toroidal axis. When the amplitude of the driving acceleration is sufficiently large, the semi-toroidal surface becomes unstable to azimuthal and radial waves. We investigate the dependence of the diverent surface wave patterns on both driving amplitude and frequency.


effect of geometry on the flapping flight of a simple wing,
click to view pdf
Lionel Rosellini and Jun Zhang
submitted,
(2007)

Abstract:
In a rotational geometry, we study the unidirectional forward motion of a symmetric wing that is flapped vertically at frequency f and amplitude a. We find that, a combined dimensionless parameter from the wing geometry (length L, thickness \delta and chord c) and flapping amplitude, \alpha, uniquely determines the forward flight speed. This scaling relationship is explained by our quasi-steady and quasi-two-dimensional model. We then apply our results from the rotational geometry to a translational forward flight and compare the outcome with biological locomotion. In particular, the Strouhal number (St = af/U) for a load-free wing is found in the range of 0.30. We further investigate the so-called ground effect, as the wing flaps close to the horizontal boundaries, which increases the forward flight speed.


hovering of a passive body in an oscillating airflow,
click to view pdf
Stephen Childress, Nicolas Vandenberghe and Jun Zhang
Physics of Fluids, 18
, 117103 (2006)

Abstract:
Small flexible bodies are observed to hover in an oscillating air column. The air is driven by a large speaker at frequencies in the range 1065 Hz at amplitudes 15 cm. The bodies are made of stiffened tissue paper, bent to form an array of four wings, symmetric about a vertical axis. The flapping of the wings, driven by the oscillating flow, leads to stable hovering. The hovering position of the body is unstable under free fall in the absence of the airflow. Measurements of the minimum flow amplitude as a function of flow frequency were performed for a range of self-similar bodies of the same material. The optimal frequency for hovering is found to vary inversely with the size. We suggest, on the basis of flow visualization, that hovering of such bodies in an oscillating flow depends upon a process of vortex shedding closely analogous to that of an active flapper in otherwise still air. A simple inviscid model is developed illustrating some of the observed properties of flexible passive hoverers at high Reynolds number.


dynamics of a deformable body in a fast flowing soap flow,
click to view pdf
S. Jung, K. Mareck, M. Shelley and Jun Zhang
Physical Review Letters, 97
, 134502 (2006)

Abstract:
We study the behavior of an elastic loop in a fast flowing soap film. The loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a 2D closed flexible body moving in a 2D viscous flow. The loop is distended by the flow, and above a velocity threshold of the soap film it begins to oscillate. The horizontal motion of the loop centroid can be accounted for as a simple harmonic oscillator driven by the drag force on the loop, with frequency linearly proportional to the flow velocity. We also investigate the morphology of the elastic loop under fluid drag and compare the result with other instances of flexible bodies moving in a laminar fluid.

the dynamics of a flexible loop in a quasi-2d flow,
click to view pdf
K. Mareck, S. Jung, M. Shelley and Jun Zhang
Physics of Fluids, 18, 091112 (2006)
No abstract for this work: it was selected by a panel of judges and published in the "Gallery of Fluid Motion"


on unidirectional flight of a free flapping wing,
click to view pdf
Nicolas Vandenberghe, Stephen Childress and Jun Zhang
Physics of Fluids, 18,
014102 (2006)
also selected and published by Virtual Journal of Biological Physics Research, 11(2)
(2006)

Abstract:
We study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward flight speed as observed in our previous study.


thermal convection with a freely moving top boundary,
click to view pdf
Jin-qiang Zhong and Jun Zhang
Physics of Fluids, 17
, 115105 (2005)

Abstract:
In thermal convection, coherent flow structures emerge at high Rayleigh numbers as a result of intrinsic hydrodynamic instability and self-organization. They range from small-scale thermal plumes that are produced near both the top and the bottom boundaries to large-scale circulations across the entire convective volume. These flow structures exert viscous forces upon any boundary. Such forces will affect a boundary which is free to deform or change position. In our experiment, we study the dynamics of a free boundary that floats on the upper surface of a convective fluid. This seemingly passive boundary is subjected solely to viscous stress underneath. However, the boundary thermally insulates the fluid, modifying the bulk flow. As a consequence, the interaction between the free boundary and the convective flows results in a regular oscillation. We report here some aspects of the fluid dynamics and discuss possible links between our experiment and continental drift.


heavy flags undergo spontaneous oscillations in flowing water,
click to view pdf
Michael Shelley, Nicolas Vandenberghe and Jun Zhang
Physical Review Letters, 94
, 094302 (2005)

Abstract:
We study the dynamics of heavy flexible sheets in a water flow, both to understand flapping of flags, and for its relevance to underwater animal locomotion. We find that the sheet can sharply transition from a straight state aligned with the flow, to a periodic flapping state, with bending waves traveling down the flag. We use a simple analytical model to understand the effect of fluid and structure inertia and elasticity. The model predicts a bifurcation with increasing flow speed, agreeing well with previous experiments in air and soap-films, but showing quantitative differences with our particular experiment.

This work was highlighted by New Scientist.


symmetry breaking leads to forward flapping flight,
click to view pdf
Nicolas Vandenberghe, Jun Zhang, and Stephen Childress
Journal of Fluid Mechanics, 506
, 147-155 (2004)

Abstract:
The locomotion of most fish and birds is effected by flapping wings or fins transverse to the direction of travel. According to classical inviscid aerodynamic theory, a flapping wing translating at fixed speed can generate a propulsive force. In steady forward flight, this thrust is balanced by drag. But when the Reynolds number is small, viscous forces dominate, reciprocal flapping motions are ineffective, and the translating wing can only experience a net drag. Our experimental study bridges the two realms of large and small Reynolds number and examines the transition to forward flapping flight. at intermediate Reynolds numbers, the range relevant to swimming and flying of small organisms. We study experimentally the dynamics of a wing that is .flapped. up and down but is free to move either forwards or backwards. We show that flapping flight occurs abruptly at a critical flapping frequency as a symmetry-breaking bifurcation. Beyond this bifurcation, the speed of the wing increases linearly with the flapping frequency. The experiment establishes a clear demarcation between the different strategies of locomotion at large and small Reynolds number.

Commentary on this work by Michael Hopkin that appeared in Nature: Nature, 429, 147 (2004)


how flexibility induces streamlining in a two-dimensional flow,
click to view pdf
Silas Alben, Michael Shelley, and Jun Zhang
Physics of Fluids, 16
, 1694-1713 (2004)

Abstract:
Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fibre wetted into a vertical soap-film tunnel, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformation of the fibre that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small "tip region" about the flow's stagnation point. The result is a transition from the classical U^2 drag scaling of rigid bodies to a U^4/3 drag law. The drag scaling is derived from an asymptotic expansion in the length scale of similarity, and it is found that the tip region induces the far-field behavior. The drag law persists, with a simple modification, under variations of the model suggested by the experiment, such as the addition of flow tunnel walls, and a back pressure in the wake.


drag reduction through self-similar bending of a flexible body,
click to view pdf
Silas Alben, Michael Shelley, and Jun Zhang
Nature, 420
, 479-481 (2002)

Abstract:
The classical theory of high-speed flow predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed -- for example, the rolling up of broad tree leaves in a stiff wind. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms. Experimental studies of such flow structure interactions generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data.

Commentary article on this work by Victor Steinberg that appeared in Nature: Bend and survive, Nature, 420, 479 (2002). It was also highlighted in New York Times.

flexible threads in a flowing soap film,
click to view pdf
Jun Zhang
Physics of Fluids, 13(9), S15 (2001)
No abstract for this work: published as an entry in session "Gallery of Fluid Motion"

flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind,
click to view pdf
Jun Zhang, Stephen Childress, Albert Libchaber, and Michael Shelley
Nature, 408, 835 (2000)
Abstract:
The dynamics of swimming fish and flapping flags involves a complicated interaction of their deformable shapes with the surrounding fluid flow. Even in the passive case of a flag, the flag exerts forces on the fluid through its own inertia, elastic responses, and is likewise acted on by hydrodynamic pressure and drag. But such couplings are not well understood. Here we study these interactions experimentally, using an analogous system of flexible filaments in flowing soap films. We find that, for a single filament (or 'flag') held at its upstream end and otherwise unconstrained, there are two distinct, stable dynamical states. The first is a stretched-straight state: the filament is immobile and aligned in the flow direction. The existence of this state seems to refute the common belief that a flag is always unstable and will flap. The second is the flapping state: the filament executes a sinuous motion in a manner akin to the flapping of a flag in the wind. We study further the hydrodynamically coupled interaction between two such filaments, and demonstrate the existence of four different dynamical states.

Commentary article on this work by Greg Huber that appeared in Nature: Swimming in flatsea, Nature 408, 777 (2000). It was also highlighted by a few popular science magzines.

periodic boundary motion in thermal turbulence, click to view pdf
Jun Zhang, Albert Libchaber
Phys. Rev. Lett., 84, 4361 (2000)
Abstract:
A free-floating plate is introduced in a Bnard convection cell with an open surface. It partially covers the cell and distorts the local heat flux, inducing a coherent flow that in turn moves the plate. Remarkably, the plate can be driven to a periodic motion even under the action of a turbulent fluid. The period of the oscillation depends on the coverage ratio, and on the Rayleigh number of the convective system. The plate oscillatory behavior observed in this experiment may be related to a geological model, in which continents drift in a quasiperiodic fashion.

non-Boussinesq effect: asymmetric velocity profiles in thermal convection, click to view pdf
Jun Zhang, S. Childress, and A. Libchaber
Physics of Fluids 10, 1534 (1998)
Abstract:
In thermal convection at high Rayleigh numbers, in the hard turbulent regime, a large scale flew is present. When the viscosity of the fluid strongly depends on temperature, the top-bottom symmetry is broken. In addition to the asymmetric temperature profile across the convection cell, the velocity profiles near the plate boundaries show dramatic difference from the symmetric case. We report here that the second derivative of the velocity profiles are of opposite signs in the thermal sublayers, through measurements derived from the power spectrum of temperature time-series. As a result, the stress rate applied at the plates is maintained constant within a factor of 3, while the viscosity changes by a factor of 53, in qualitative agreement with previous theory.

non-Boussinesq effect: thermal convection with broken symmetry, click to view pdf
Jun Zhang, S. Childress, and A. Libchaber
Physics of Fluids 9, 1034 (1997)
Abstract:
We investigate large Rayleigh number (106-109) and large Prandtl number (102-103) thermal convection in glycerol in an aspect ratio one cubic cell. The kinematic viscosity of the fluid strongly depends upon the temperature. The symmetry between the top and bottom boundary layers is thus broken, the so-called non-Boussinesq regime. In a previous paper Wu and Libchaber have proposed that in such a state the two thermal boundary layers adjust their length scales so that the mean hot and cold temperature fluctuations are equal in the center of the cell. We confirm this equality. A simplified two-dimensional model for the mean center temperature based on an equation for the thermal boundary layer is presented and compared with the experimental results. The conclusion is that the central temperature adjusts itself so that the heat fluxes from the boundary layers are equal, temperature fluctuations at the center symmetrical, at a cost of very different temperature drops and Rayleigh number for each boundary.

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