Research Highlights
Wavebased liquidinterface metamaterials
This paper demonstrates a method of remotely shaping
the trajectories of floating particles on a liquidgas interface.
It uses linear surface waves and relies solely on hydrodynamic forces.
A rotating wave field is produced in a square geometry by the
orthogonal superposition of two smallamplitude, threedimensional (3D) standing waves.
The local angular momentum of the rotating wave field is transferred to the matter and determines the Lagrangian drift of particles along closed paths.
The mechanism produces particle trajectories
in the form of a spatially periodic lattice of nested orbitals.
It offers a high degree of control over the particle motion
and the ability to confine particles to spatially periodic cells.
Such dynamic patterns, a mirror image of the concept of metamaterials, are scalable and biocompatible. They can be used in assembly applications, conversion of wave energy into mean twodimensional flows and for organising the motion of active swimmers.
Nature Communications 7 , 14325 (2017).
DOI: 10.1038/ncomms14325
(link)
Generation and reversal of surface flows by propagating waves
We show here that water surface waves can generate surface flows.
Propagating waves, produced by an oscillating wave maker, become nonlinear at high amplitude
and break up into solitonlike pulses. As a result, the motion of floaters on the surface
reverses direction. Small floating objects move towards the wave source, against the wave propagation direction.
The geometry of the flow depends on the shape of the wave. It can be controlled
by the shape of the wave maker and by the nonlinearity of the wave field in front of the wave maker.
The ability of waves to produce surface flows opens an array of opportunities,
for example to collect water surface pollutants, stop spreading oil spills, or it may give a clue
on how onshore ocean swell can produce rip currents on coastal beaches.
Nature Physics 10, 658663 (2014).
doi:10.1038/nphys3041 (link)
Lagrangian particle transport in 2D turbulence
Transport of mass, heat, and momentum in turbulent flows by far exceeds that in stable laminar fluid motions.
Since turbulence is a state of a flow dominated by a hierarchy of scales, it is not clear which of these scales
mostly affect particle dispersion. Also, it is not uncommon that turbulence coexists with coherent vortices.
Here we report on Lagrangian statistics in laboratory twodimensional turbulence. Our results provide direct
experimental evidence that fluid particle dispersion is determined by a single measurable Lagrangian scale related
to the forcing scale. These experiments offer a new way of predicting dispersion in turbulent flows in which one
of the low energy scales possesses temporal coherency. The results are applicable to oceanographic and atmospheric
data, such as those obtained from trajectories of freedrifting instruments in the ocean.
Nature Communications 4:2013, doi: 10.1038/ncomms3013 (2013).
(PDF)
Water surface ripples: waves or quasiparticles?
We show that ripples on the surface of deep water which are driven parametrically by monochromatic
vertical vibration represent ensembles of oscillating solitons, or quasiparticles, rather than waves.
Horizontal mobility of oscillons determines the broadening of spectral lines and transitions from chaos
to regular patterns. It is found that microscopic additions of proteins to water dramatically affect
the oscillon mobility and drive transitions from chaos to order. The shape of the oscillons in physical
space determines the shape of the frequency spectra of the surface ripple.
Phys.Rev.Lett. 108, 034502 (2012) (PDF)
Upscale energy transfer in thick turbulent fluid layers
When a thick fluid, such as the Earth’s atmosphere, is driven simultaneously by a largescale
twodimensional vortex and smallscale threedimensional turbulence, experiments show that the
largescale flow dominates. Turbulence is thus confined to two dimensions, giving rise to an
upscale energy cascade that powers the intermediate and largescale flows.
Nature Physics 7, 321324 (2011)  doi:10.1038/nphys1911 (PDF)
Turbulence decay rate as a measure of flow dimensionality
The dimensionality of turbulence in fluid layers determines their properties.
We show that eddy viscosity, which appears as a result of
threedimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes
the deviation of damping from the one derived using a quasitwodimensional model, can be used as a
measure of the flow dimensionality. When the anomaly
coefficient becomes high, the turbulent inverse energy cascade is suppressed.
Phys.Rev.Lett., 105, 264501 (2010)
Modulation instability and capillary wave turbulence
Broad spectra characterize many turbulent systems.
In the weak turbulence theory (WTT) spectral transfer is attributed to the energy cascades.
In this paper we present the first comprehensive experimental tests of the WTT of capillary waves.
EPL, 91, 14002 (2010)
Capillary rogue waves
Extreme wave events, also referred to as rogue or freak
waves, are mostly known as an oceanic phenomenon responsible
for a large number of maritime disasters. These
waves, which have heights and steepness much greater
than expected from the sea state, have become a focus
of intense research in the last decade. Here we report the first observation of extreme
wave events in nonlinear capillary waves.
Phys.Rev.Lett., 104, 104503 (2010)
Spectral condensation of twodimensional turbulence
Turbulent flows in thin layers of fluids support the energy transfer from smaller to larger scales.
We study spectral condensation of quasitwodimensional turbulence, a process somewhat
similar to the BoseEinstein condensation. It leads to
the formation of a large vortex and represents an important example of
turbulence selforganization.
Phys. Rev. E, 71, 046409 (2005);
Phys. Fluids, 21, 125101 (2009)
Phase randomization of threewave interactions in capillary waves
Capillary waves, which
belong to a short wave branch of surface waves
(<10 mm), play an important role in the surface wave
physics in the ocean. They are also of interest from a
general point of view as an example of nonlinear strongly
dispersive waves. Here we study nonlinear interactions in capillary waves and
show that breaking of continuous waves into ensembles of envelope solitons leads to their phase randomization and to the change in
the nature of threewave interactions.
Phys.Rev.Lett., 103, 064502 (2009)
Effects of large flows on 2D turbulence
Turbulence often coexists with flows
coherent across the system size. Flows, either externally imposed or selfgenerated,
greatly affect underlying turbulence.
Understanding interaction between turbulence and a mean
flow is of prime importance for many problems in atmospheric physics, astrophysics,
geophysics, plasma confinement, etc.
Phys.Rev.Lett., 99, 164502 (2007)
Phys.Rev.Lett., 101, 194504 (2008)
Improved plasma confinement and turbulencedriven zonal flows
Turbulence adversely affects plasma confinement by magnetic fields. However plasma may transit from low (L) to improved
(or high, or H) mode. This regime is highly desirable for future plasma fusion reactors.
Improved confinement, or Hmode, is characterized by the formation of transport barriers and turbulence suppression.
Hmodes have been extensively studied by the group in the H1 heliac.
Key physical mechanisms related to the LH transitions have been discovered. Among them is the turbulence selfregulation by zonal flows
correlated with formation of transport barriers.
Phys.Rev.Lett, 97, 255003 (2006);
Phys.Rev.Lett, 93, 125003 (2004)
Phys.Rev.Lett, 91, 155001 (2003);
NewJ.Phys., 4, 30 (2002)
Phys.Rev.Lett, 77, 4190 (1996);
Phys.Rev.Lett, 79, 2690 (1997)

Recent Publications
N. Francois, H. Xia, H. Punzmann, P.W. Fontana and M. Shats
Wavebased liquidinterface metamaterials,
Nature Communications 7, 14325 (2017).
(link, Free online)
N. Francois, H. Xia, H. Punzmann, B. Faber and M. Shats
Braid Entropy of TwoDimensional Turbulence,
Scientific Reports 5, 18564 (2015).
(link, Free online)
(PDF)
N. Francois, H. Xia, H. Punzmann and M. Shats
Waveparticle interaction in the Faraday waves,
The European Physical Journal E 38, 106 (2015).
(link)
(PDF)
N. Francois, H. Xia, H. Punzmann, T. Combriat and M. Shats
Inhibition of wavedriven twodimensional turbulence by viscoelastic films of proteins,
Physical Review E 92, 023027 (2015).
(link) (PDF)
Punzmann H., Francois N., Xia H., Falkovich G. and Shats M.
Generation and reversal of surface flows by propagating waves,
Nature Physics 10, 658663 (2014).
(link) (PDF)
Xu H., Pumir A., Falkovich G., Bodenschatz E., Shats M., Xia H., Francois N., and Boffetta G.
Flightcrash events in turbulence,
Proceedings of the National Academy of Science of the USA 111, 75587563 (2014). doi:10.1073/pnas.1321682111 (Link) (PDF)
Francois N., Xia H., Punzmann H., Ramsden S., and Shats M.
Threedimensional fluid motion in Faraday waves: Creation of vorticity and generation of twodimensional turbulence,
Physical Review X 4, 021021 (2014) (Link, free online) (PDF)
Xia H., Francois N., Punzmann H., and Shats M.
Taylor particle dispersion during transition to fully developed twodimensional turbulence,
Physical Review Letters 112, 104501 (2014) (PDF)
Xia H.
Lagrangian correlation and spectra in 2D turbulence,
Int. J. Mod. Phys.: Conf. Series 34, 1460378 (2014) (PDF)
Shats M., Francois N., Xia H., Punzmann H.
Turbulence driven by Faraday surface waves,
Int. J. Mod. Phys.: Conf. Series 34, 1460379 (2014) (PDF)
Xia H., Francois N., Punzmann H., and Shats M.
Lagrangian scale of particle dispersion in turbulence,
Nature Communications 4:2013, doi: 10.1038/ncomms3013 (2013).
(PDF)
Francois N., Xia H., Punzmann H., and Shats M.
Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves,
Physical Review Letters 110, 194501 (2013) (PDF)
Xia H., Maimbourg T., Punzmann H., and Shats M.
Oscillon dynamics and rogue wave generation in Faraday surface ripples,
Physical Review Letters 109, 114502 (2012) (PDF)
Xia H., and Shats M.
Structure formation in spectrally condensed turbulence,
Int. J. Mod. Phys. Conf. Ser. 19, 257261 (2012) (PDF)
Shats M., Xia H., Byrne D.
Turbulence in thick layers,
Int. J. Mod. Phys. Conf. Ser. 19, 390395 (2012) (PDF)
Xia H., and Shats M.
Propagating solitons generated by localized perturbations on the surface of deep water,
Physical Review E 85, 026313 (2012) (PDF)
Shats M., Xia H., and Punzmann H.
Parametrically excited water surface ripples as ensembles of oscillons,
Physical Review Letters 108, 034502 (2012) (PDF)
Xia H., Shats M. and Falkovich G.
Turbulence in fluid layers,
Journal of Physics: Conference Series 318, 012001 (2011) doi:10.1088/17426596/318/1/012001
[PDF] (link)
Byrne D., Xia H. and Shats M.
Robust inverse energy cascade and turbulence structure in threedimensional layers of fluid,
Physics of Fluids 23, 095109 (2011) doi:10.1063/1.3638620
[PDF] (link)
Xia H., Byrne D., Falkovich G. & Shats M.
Upscale energy transfer in thick turbulent fluid layers,
Nature Physics 7, 321324 (2011),
doi:10.1038/nphys1910 (PDF)
(link)
Shats M., Byrne D., Xia H.
Turbulence decay rate as a measure of flow dimensionality, Physical Review Letters,
105, 264501 (2010) [PDF]
Xia H., Shats M., Punzmann H.
Modulation instability and capillary wave turbulence, EPL,
91, 14002 (2010) [PDF]
Shats M., Punzmann H., Xia H. Capillary rogue waves,
Physical Review Letters, 104, 104503 (2010) [PDF]
