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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 spherebound orbits,
click to review pdf
D. Takagi, J. Palacci, A. Braunschweig, M. Shelley and J. Zhang
Soft Matter 10, 1784 (2014)

Abstract:
Selfpropelled particles can exhibit surprising nonequilibrium behaviors, and how they interact with
obstacles or boundaries remains an important open problem. Here we show that chemically propelled microrods
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 shortrange,
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 torquefree 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 activitydriven interactions of selfpropelled particles
with passive objects, and brings into question the use of colloidal tracers as probes of active matter.

selfsimilar 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 selfsimilar
evolution of the body, with an emerging quasitriangular 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 selfpropelled rods undergoing fluctuationdriven 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 fluctuationdriven 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 longterm effects on macroscopic dispersion.

fluidstructure 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
IEEEASME 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 inhouse designed power electronics for lowfrequency
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 microorganisms 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 fluidfilled arrays of micropillars 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 lifelike 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 nonNewtonian 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 counterrotating 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 pyramidshaped 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
bottomheavy flyers.

flapping and bending bodies interacting with fluid flows,
click to review pdf
Michael Shelley and Jun Zhang
Annual Review of Fluid Mechanics, 43, 449465 (2011)

Abstract:
The flapping or bending of a flexible planar structure in a surrounding fluid flow, which includes
the flapping of flags and the selfstreamlining of flexible bodies, constitutes a central problem
in the field of fluidbody 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 shearthickening 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 quasisteady 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).

selfinduced 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 manybody interactions mediated by
thermal convection, which gives rise to surprising robust oscillations between dierent largescale
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 scinews 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 (19812008), 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
thrustgeneration 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 selfsustained
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 JinQiang 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
JinQiang Zhong and Jun Zhang
Physical Review E, 76, 016307 (2007)

Abstract:
Based on our previous experimental study, we present a onedimensional, 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 fullscale simulations.

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

Abstract:
We study experimentally the dynamical states of a freelymoving, floating heat blanket
that couples with a thermally convective fluid. The floating boundary modifies the largescale
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 lowdimensional model that
appears to capture the underlying mechanism of the coupled system.

standing surface waves on a semitoroidal 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 semitoroidal 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 semitoroidal 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 quasisteady and quasitwodimensional 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 loadfree wing is found in the range of 0.30.
We further investigate the socalled 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 selfsimilar 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 quasi2d 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
Jinqiang 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 selforganization. They range from smallscale thermal plumes that are produced
near both the top and the bottom boundaries to largescale 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 soapfilms, 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, 147155 (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 symmetrybreaking 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 twodimensional flow,
click to view pdf
Silas Alben, Michael Shelley, and Jun Zhang
Physics of Fluids, 16 , 16941713 (2004)

Abstract:
Recent work in biofluid 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 soapfilm 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 freestreamline models that couple fluid and elastic forces and solve them in an efficient numerical
scheme. Shape selfsimilarity 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 farfield 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 selfsimilar bending of a flexible body, click
to view pdf
Silas Alben, Michael Shelley, and Jun Zhang
Nature, 420, 479481 (2002)

Abstract:
The classical theory of highspeed 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 selfsimilar; for such configurations, the drag scales with
the length of selfsimilarity, 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 onedimensional
flags in a twodimensional 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 stretchedstraight 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 freefloating 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.

nonBoussinesq 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 topbottom 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 timeseries. 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.

nonBoussinesq effect: thermal convection with broken symmetry,
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Jun Zhang, S. Childress, and A. Libchaber
Physics of Fluids 9, 1034 (1997) 
Abstract:
We investigate large Rayleigh number (106109) and large Prandtl number (102103) 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 socalled nonBoussinesq 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 twodimensional 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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