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RayleighBenard thermal convection perturbed by a horizontal heat flux,
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Huang, J.Z. and Zhang J.
J. Fluid Mech. 954, R2 (2023)

Abstract:
In Rayleigh Benard convection, it has been found that the amount of heat passing through the fluid has a powerlaw
dependence on the imposed temperature difference. Modifying this dependence, either enhancing or reducing the heat
transfer capability of fluids, is important in many scientific and practical applications. Here, we present a simple
means to control the vertical heat transfer in Rayleigh Benard convection by injecting heat through one lateral side
of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates
the largescale circulation, and increases the heat transfer rate in the vertical direction. Our numerical and
theoretical studies demonstrate how a classical Rayleigh Benard convection responds to such a perturbation when the
system is near or well above the onset of convection.

lateral flow interactions enhance speed and stabilize formations of flapping swimmers,
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Newbolt J, Zhang J, and Ristroph L.
Physical Review Fluids 7, L061101 (2022)

Abstract:
While classic hydrodynamic models predict ordered formations for fish schools, observations show that schools are
seemingly disordered. Our experiments on robotic swimmers may help to reconcile this discrepancy by showing that
many different formations all emerge spontaneously and are stabilized due to flow interactions. Surprisingly, these
locked states extend almost twice as far downstream for laterally displaced swimmers as for those in line. We also
observe significant boosts in swimming speed, up to 60% faster than an isolated swimmer, for sidebyside formations.
These findings demonstrate that benefits such as group cohesion and speed enhancement arise naturally via flow
interactions and for the diverse relative arrangements seen in schools.

enhanced clamshell swimming with asymmetric beating at low Reynolds number,
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Hu SY, Zhang J, and Shelley M.
Soft Matter 18, 3605 (2022)

Abstract:
A single flexible filament can be actuated to escape from the scallop theorem and generate net propulsion
at low Reynolds number. In this work, we study the dynamics of a simple boundarydriven multifilament
swimmer, a twoarm clamshell actuated at the hinged point, using a nonlocal slender body approximation
with hydrodynamic interactions. We first consider an elastic clamshell consisted of flexible filaments
with intrinsic curvature, and then build segmental models consisted of rigid segments connected by different
mechanical joints with different forms of response torques. The simplicity of the system allows us to fully
explore the effect of various parameters on the swimming performance. Optimal included angles and
elastoviscous numbers are identified. The segmental models capture the characteristic dynamics of the
elastic clamshell. We further demonstrate how the swimming performance can be significantly enhanced
by the asymmetric beating patterns induced by biased torques.

open capillary siphons,
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Wang KZ, Sanaei P, Zhang J, and Ristroph L.
J. Fluid Mech. 932, R1 (2022)

Abstract:
Flow in the inverted Ushaped tube of a conventional siphon can be established and maintained only if
the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely
open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated
by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce
a more controlled system consisting of grooves in a wetting solid, formed here by pressing together
hookshaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing
behaviour different from the conventional siphon. The flux saturates when the height difference between
the two container’s free surfaces is large; it also has a strong dependence on the climbing height from
the source container’s free surface to the apex. A onedimensional theoretical model is developed, taking
into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and
driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests
hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating
principle and characteristics of capillary siphoning revealed here can inform biological phenomena and
engineering applications related to directional fluid transport.

enhanced heat transport in thermal convection with suspensions of rodlike expandable particles,
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Hu SY, Wang KZ, Jia LB, Zhong JQ and Zhang J.
J. Fluid Mech. 928, R1 (2021)

Abstract:
Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold
places. Here, we experimentally study the RayleighBenard convection of aqueous glycerol solution in a cubic
cell with suspensions of rodlike particles made of polydimethylsiloxane (PDMS). The particles are inertial
due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the
particles is three times larger than that of the background fluid. This contrast makes the suspended particles
lighter than the local fluid in hot regions and heavier in cold regions. The heat transport is enhanced at
relatively large Rayleigh number (Ra) but reduced at small Ra. We demonstrate that the increase of Nusselt
number arises from the particleboundary layer interactions: the particles act as "active" mixers of the flow
and temperature fields across the boundary layers.

levy walks and path chaos in the dispersal of elongated structures moving across cellular vortical flows,
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Hu SY, Chu JJ, Shelley M, Zhang J.
Phys. Rev. Lett. 127, 074503 (2021)

Abstract:
In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show
simple random walks through their stretchcoil interactions with flow stagnation points. Here, we study the
dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we
find a surprising variety of longtime transport behavior—random walks, ballistic transport, and trapping—
depending upon the filament’s relative length and effective flexibility. Moreover, we find that filaments
execute L´evy walks whose diffusion exponents generally decrease with increasing filament length, until
transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid
filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos.
Fast filament dispersal is related to an underlying geometry of “conveyor belts.” Evidence for these various
transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and
transporting a flexible ribbon.

metallic microswimmers driven up the wall by gravity,
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Brosseau, Usabiaga, Lushi, Wu, Ristroph, Ward, Shelley and Zhang
Soft Matter. 17, 6597 (2021)

Abstract:
Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show
that tailheavy 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 foreaft drag asymmetry induced by
hydrodynamic interactions with the wall.

streaming controlled by meniscus shape,
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Huang, Wolfe, Zhang and Zhong
J. Fluid Mech. 895, A1 (2020)

Abstract:
Surface waves called meniscus waves often appear in systems that are close to the
capillary length scale. Since the meniscus shape determines the form of the meniscus
waves, the resulting streaming circulation has features distinct from those caused by
other capillary–gravity waves recently reported in the literature. In the present study,
we produce symmetric and antisymmetric meniscus shapes by controlling boundary
wettability and excite meniscus waves by oscillating the meniscus vertically. The
symmetric and antisymmetric configurations produce different surface capillary–gravity
wave modes and streaming flow structures. The rootmeansquare speed of the
streaming circulation increases with the second power of the forcing amplitude in
both configurations. The flow symmetry of streaming circulation is retained under the
symmetric meniscus, while it is lost under the antisymmetric meniscus. The streaming
circulation pattern beneath the meniscus observed in our experiments is qualitatively
explained using the method introduced by Nicolás & Vega and Gordillo & Mujica.

relating rheotaxis and hydrodynamic actuation using asymmetric goldplatinum phoretic rods,
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Brosseau, Usabiaga, Lushi, Wu, Ristroph, Zhang, Ward, and Shelley
Phys. Rev. Lett. 123, 178004 (2019)

Abstract:
We explore the behavior of micronscale autophoretic Janus (Au/Pt) rods, having various Au/Pt length
ratios, swimming near a wall in an imposed background flow. We find that their ability to robustly orient
and move upstream, i.e., to rheotax, depends strongly on the Au/Pt ratio, which is easily tunable in
synthesis. Numerical simulations of swimming rods actuated by a surface slip show a similar rheotactic
tunability when varying the location of the surface slip versus surface drag. The slip location determines
whether swimmers are pushers (rear actuated), pullers (front actuated), or in between. Our simulations and
modeling show that pullers rheotax most robustly due to their larger tilt angle to the wall, which makes
them responsive to flow gradients. Thus, rheotactic response infers the nature of difficult to measure flow
fields of an active particle, establishes its dependence on swimmer type, and shows how Janus rods can be
tuned for flow responsiveness. [*Editor's Suggestion; *Featured in Physics]

the role of shapedependent flight stability in the origin of oriented meteorites,
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Amin, Huang, Hu, Zhang and Ristroph
PNAS 116, 16180 (2019)

Abstract:
The atmospheric ablation of meteoroids is a striking example of the reshaping of a solid object due to its motion through a
fluid. Motivated by meteorite samples collected on Earth that suggest fixed orientation during flight—most notably the conical
shape of socalled oriented meteorites—we hypothesize that such forms result from an aerodynamic stabilization of posture
that may be achieved only by specific shapes. Here, we investigate this issue of flight stability in the parallel context of
fluid mechanical erosion of clay bodies in flowing water, which yields shapes resembling oriented meteorites.We conduct laboratory
experiments on conical objects freely moving through water and fixed within imposed flows to determine the dependence
of orientational stability on shape. During free motion, slender cones undergo postural instabilities, such as inversion and tumbling,
and broad or dull forms exhibit oscillatory modes, such as rocking and fluttering. Only intermediate shapes, including
the stereotypical form carved by erosion, achieve stable orientation and straight flight with apex leading. We corroborate these
findings with systematic measurements of torque and stability potentials across cones of varying apex angle, which furnish
a complete map of equilibrium postures and their stability. By showing that the particular conical form carved in unidirectional
flows is also posturally stable as a free body in flight, these results suggest a selfconsistent picture for the origin of oriented
meteorites.

the dynamics of an insulating plate over a thermally convecting fluid and its implication for continent movement over convective mantle,
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Mao, Zhong, and Zhang
Journal of Fluid Mechanics 868, 286 (2019)

Abstract:
Continents exert a thermal blanket effect to the mantle underneath by locally accumulating heat and modifying the flow structures,
which in turn affects continent motion. This dynamic feedback is studied numerically with a simplified model of an insulating plate
over a thermally convecting fluid with infinite Prandtl number at Rayleigh numbers of the order of 10^6. Several plate–fluid coupling
modes are revealed as the plate size varies. In particular, small plates show long durations of stagnancy over cold downwellings.
Between long stagnancies, bursts of velocity are observed when the plate rides on a single convection cell. As plate size increases,
the coupled system transitions to another type of shortlived stagnancy, in which case hot plumes develop underneath. For an even
larger plate, a unidirectional moving mode emerges as the plate modifies impeding flow structures it encounters while maintaining a
single convection cell underneath. These identified modes are reminiscent of some real cases of continent–mantle coupling. Results
show that the capability of a plate to overcome impeding flow structures increases with plate size, Rayleigh number and intensity of
internal heating. Compared to cases with a fixed plate, cases with a freely drifting plate are associated with higher Nusselt number
and more convection cells within the flow domain..

flow interactions between uncoordinated flapping swimmers give rise to group cohesion,
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Newbolt, Zhang, and Ristroph
PNAS 116, 2419 (2019)

Abstract:
Many species of fish and birds travel in groups, yet the role of fluidmediated interactions in schools and flocks is not fully
understood. Previous fluid dynamical models of these collective behaviors assume that all individuals flap identically, whereas
animal groups involve variations across members as well as active modifications of wing or fin motions. To study the roles
of flapping kinematics and flow interactions, we design a minimal robotic “school” of two hydrofoils swimming in tandem.
The flapping kinematics of each foil are independently prescribed and systematically varied, while the forward swimming motions
are free and result from the fluid forces. Surprisingly, a pair of uncoordinated foils with dissimilar kinematics can swim together
cohesively—without separating or colliding—due to the interaction of the follower with the wake left by the leader. For equal
flapping frequencies, the follower experiences stable positions in the leader’s wake, with locations that can be controlled by
flapping amplitude and phase. Further, a follower with lower flapping speed can defy expectation and keep up with the leader,
whereas a fasterflapping follower can be buffered from collision and oscillate in the leader’s wake. We formulate a reducedorder
model which produces remarkable agreement with all experimentally observed modes by relating the follower’s thrust to its flapping
speed relative to the wake flow. These results show how flapping kinematics can be used to control locomotion within wakes, and
that flow interactions provide a mechanism which promotes group cohesion.

stochastic dynamics of fluidstructure interaction in turbulent thermal convection,
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Huang, Zhong, Zhang, and Mertz
Journal of Fluid Mechanics 854, R5 (2018)

Abstract:
The motion of a freemoving plate atop turbulent thermal convection exhibits diverse
dynamics that displays characteristics of both deterministic and chaotic motions. Early
experiments performed by Zhong and Zhang found two states existing for a plate floating
on convective fluid in a rectangular tank. They proposed a piecewise smooth physical
model (ZZ model) that successfully captures this transition of states. However, their
model was deterministic and therefore could not describe the stochastic behaviors. In
this study, we combine the ZZ model with a novel approach that models the stochastic
aspects through a variational inequality structure. With the powerful mathematical
tools for stochastic variational inequalities, the properties of the Markov process
and corresponding Kolmogorov equations could be studied both numerically and analytically.
Moreover, this framework also allows one to compute the transition probabilities. Our
present work captures the stochastic aspects of the two aforementioned boundaryfluid
coupling states, predicts the stochastic behaviors and shows excellent qualitative and
quantitative agreement with the experimental data.

guiding microscale swimmers using teardropshaped posts,
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Wykes, Zhong, Tong, Adachi, Liu, Ristroph, Ward, Shelley and Zhang
Soft Matter 13, 4681 (2017)

Abstract:
The swimming direction of biological or artificial microscale swimmers tends to be randomised over long
timescales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve
directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein,
we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial
swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with
teardropshaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside
the post perimeter for long times before leaving. The rods experience a higher rate of departure from the
higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases
with swimming speed and can be translated into a macroscopic directional motion over long times by using
arrays of teardropshaped posts aligned along a single direction. This method provides a protocol for
concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers
to transport cargo to desired locations. [* Featured on the cover of Soft Matter, 13(27) 2017]

footprints of a flapping wing,
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Jun Zhang
J. Fluid Mech. 818, 14 (2017)

Abstract:
Birds have to flap their wings to generate the needed thrust force, which powers them
through the air. But how exactly do flapping wings create such force, and at what
amplitude and frequency should they operate? These questions have been asked by
many researchers. It turns out that much of the secret is hidden in the wake left
behind the flapping wing. Exemplified by the study of Andersen et al. (J. Fluid Mech.,
vol. 812, 2017, R4), close examination of the flow pattern behind a flapping wing
will inform us whether the wing is towed by an external force or able to generate
a net thrust force by itself. Such studies are much like looking at the footprints of
terrestrial animals as we infer their size and weight, figuring out their walking and
running gaits. A map that displays the collection of flow patterns after a flapping wing,
using flapping frequency and amplitude as the coordinates, offers a full picture of its
flying ‘gaits’.

flow interaction lead to orderly formation of flapping wings in forward flight,
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S. Ramananarivo, F. Fang, A. Oza, J. Zhang and L. Ristroph
Phys. Rev. Fluids 1, 071201(R) (2016)

Abstract:
Classic models of fish schools and flying formations of birds are built on the hypothesis
that the preferred locations of an individual are determined by the flow left by its upstream
neighbor. Lighthill posited that arrangements may in fact emerge passively from hydro or
aerodynamic interactions, drawing an analogy to the formation of crystals by intermolecular
forces. Here, we carry out physical experiments aimed at testing the Lighthill conjecture and
find that selfpropelled flapping wings spontaneously assume one of multiple arrangements
due to flow interactions.Wings in a tandem pair select the same forward speed, which tends
to be faster than a single wing, while maintaining a separation distance that is an integer
multiple of the wavelength traced out by each body. When perturbed, these locomotors
robustly return to the same arrangement, and direct hydrodynamic force measurements
reveal springlike restoring forces that maintain group cohesion. We also use these data
to construct an interaction potential, showing how the observed positions of the follower
correspond to stable wells in an energy landscape. Flow visualization and vortexbased
theoretical models reveal coherent interactions in which the follower surfs on the periodic
wake left by the leader. These results indicate that, for the highReynoldsnumber flows
characteristic of schools and flocks, collective locomotion at enhanced speed and in orderly
formations can emerge from flow interactions alone. If true for larger groups, then the view
of collectives as ordered states of matter may prove to be a useful analogy.

linear drag law for highReynoldsnumber flow past an oscillating body,
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N. Agre, S. Childress, J. Zhang and L. Ristroph
Phys. Rev. Fluids 1, 033202 (2016)

Abstract:
An object immersed in a fast flow typically experiences fluid forces that increase with the
square of speed. Here we explore how this highReynoldsnumber forcespeed relationship
is affected by unsteady motions of a body. Experiments on disks that are driven to
oscillate while progressing through air reveal two distinct regimes: a conventional quadratic
relationship for slow oscillations and an anomalous scaling for fast flapping in which the
timeaveraged drag increases linearly with flow speed. In the linear regime, flow visualization
shows that a pair of counterrotating vortices is shed with each oscillation and a model
that views a train of such dipoles as a momentum jet reproduces the linearity.We also show
that appropriate scaling variables collapse the experimental data from both regimes and for
different oscillatory motions into a single dragspeed relationship. These results could provide
insight into the aerodynamic resistance incurred by oscillating wings in flight and they
suggest that vibrations can be an effective means to actively control the drag on an object.

dynamic selfassembly of microscale rotors and swimmers,
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M. Wykes, J. Palacci, T. Adachi, L. Ristroph, X. Zhong, M. Ward, J. Zhang and M. Shelley
Soft Matter 12, 4584 (2016)

Abstract:
Biological systems often involve the selfassembly of basic components into complex and functioning
structures. Artificial systems that mimic such processes can provide a wellcontrolled setting to explore
the principles involved and also synthesize useful micromachines. Our experiments show that immotile,
but active, components selfassemble into two types of structure that exhibit the fundamental forms of
motility: translation and rotation. Specifically, micronscale 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 runandtumble motion.

enhanced heat transport in partitioned thermal convection,
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Y. Bao, J. Chen, B.F. Liu, Z.S. She, J. Zhang and Q. Zhou
Journal of Fluid Mechanics 784, R5 (2015)

Abstract:
Enhancing heat transport across a fluid layer is of fundamental interest as well as of great technological
importance. For decades, RayleighB\'{e}nard convection has been a paradigm for the study of convective heat
transport, and how to improve its overall heattransfer efficiency is still an open question. Here we report
an experimental and numerical study that reveals a novel mechanism that leads to much enhanced heat transport.
When vertical partitions are inserted into a convection cell with thin gaps left open between partition walls
and the cooling/heating plates, it is found that the convective flow becomes selforganized and more coherent,
leading to an unprecedented heattransport enhancement. In particular, our experiments show that with 6
partition walls inserted the heat flux can be increased by about $30\%$. Numerical simulations show a remarkable
heatflux enhancement of up to 2.3 times (with 28 partition walls) that without any partitions.

comparative flow visualization for steady and unsteady motions of a disk through a fluid,
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N. Agre, S. Childress, J. Zhang and L. Ristroph
Physics of Fluids 27, 091103 (2015)

Abstract:
On flow visualization of around a flapped disk. This publication follows the competition  the Galley of Fluid
Motion  at the APS/DFD meeting 2014.

ratcheting fluid with geometric anisotropy,
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B. Thiria and J. Zhang
Applied Physics Letters 106, 054106 (2015)

Abstract:
We investigate a mechanism that effectively transports fluids using vibrational motion imposed onto fluid boundary
with anisotropy. In our experiment, two asymmetric, sawtoothlike structures are placed facing each other and form
a corrugated fluid channel. This channel is then forced to open and close periodically. Under reciprocal motion,
fluid fills in the gap during the expansion phase of the channel and is then forced out during contraction. Since
the fluid experiences different impedence when flowing in different directions, the stagnation point that separates
flows of two directions changes within each driving period. As a result, fluid is transported unidirectionally. This
ratcheting effect of fluid is demonstrated through our measurements and its working principle discussed in some detail.

lateral line layout correlates with the differential hydrodynamic pressure on swimming fish,
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L. Ristroph, J. Liao and J. Zhang
Phys. Rev. Lett. 114, 018102 (2015)

Abstract:
The lateral line of fish includes the canal subsystem that detects hydrodynamic pressure gradients and is
thought to be important in swimming behaviors such as rheotaxis and prey tracking. Here, we explore the
hypothesis that this sensory system is concentrated at locations where changes in pressure are greatest
during motion through water. Using highfidelity models of rainbow trout, we mimic the flows encountered
during swimming while measuring pressure with fine spatial and temporal resolution. The variations in
pressure for perturbations in body orientation and for disturbances to the incoming stream are seen to
correlate with the sensory network. These findings support a view of the lateral line as a “hydrodynamic
antenna” that is configured to retrieve flow signals and also suggest a physical explanation for the nearly
universal sensory layout across diverse species.

hydrodynamic capture of microswimmers into spherebound orbits,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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.
This work was highlighted on the cover of Physical Review Letters.

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,
click to view pdf
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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