Wave turbulence
is a domain rapidly expanding for several years. It concerns
the study of the dynamical and statistical properties of a
set of numerous waves in interaction. This is a ubiquitous
phenomenon that occurs in various situations on very different scales: from spin waves in solids,
internal or surface waves in oceanography up to plasma waves
in astrophysics.
Wave
turbulence theory, also called weak turbulence,
assumes that the energy transfer is governed by
resonant interaction between waves leading to an
energy cascade from large (forcing) scales up to
small (dissipative) ones. Although this theory from the end of the 60s can
be applied to nearly all fields of physics
involving weakly nonlinear waves, well-controlled laboratory
experiments on wave turbulence remained few. The
last years saw an important experimental effort,
particularly in France, notably to probe the
limits of validity of the theory based on very
restrictive hypotheses (infinite size effects,
weak nonlinearity, scale separation, constant
energy flux, local interactions...). Experiments show
the limitations of the current theoretical
framework, which in return, arouses a theoretical
and numerical renewed interest.
Our projects are funded by ANR Turbonde
2008-2011, ANR Turbulon 2012-2016 and ANR Dysturb 2017-2021.
Gravity-capillary wave turbulence: Laboratory
experiments
We experimentally study
and characterize gravity-capillary wave turbulence on
the surface of a fluid to better understand the basic
mechanisms of energy transfer between waves.
We have observed in
laboratory the regime of gravity-capillary
wave turbulence [1],
and have reported the first observation of
intermittency in wave turbulence [2]. The intermittency is
shown to not come from some coherent
structures at large scale (wavebreakings,
capillary bursts on steep gravity waves) [10,11].
Moreover, two major experimental challenges
have been faced: the measurement of injected
power [3],
and to measure the wave field fully resolved
in space and time [12]. At
the time, those quantities were not yet been
measured directly for wave turbulence on the
surface of a fluid. Two main results have
then been obtained: (i) Energy transfer
mechanisms are not restricted to purely
resonant wave interactions, as assumed by
the theory, but involved other mechanisms
related to the presence of strong nonlinear
waves (sharp crested waves, bound waves,
...) [12];
(ii) The system shows large injected power
fluctuations within the fluid [3],
fluctuations not taken into account by weak
turbulence theory. We showed that the
distribution of injected power fluctuations
is well described by a simple model [7]. A book chapter
has been also published
on the fluctuations in
wave turbulence [19],
as well as a
review on wave turbulence
[6, 9].
We have then reported the first observation in
laboratory of the direct
gravity-capillary cascade when the fluid
is not in a deep-water regime [14]. The study of
non-stationary regime of capillary wave
turbulence, when the forcing is stopped,
led to the first observation of decay wave
turbulence [16]. Another
optical method (different form Fourier
Transform Profilometry used in [12])
called Diffusing
Light Videography, has
been used to reconstruct the capillary wave
field both in time and space. We have
highlighted the role of strongly nonlinear
capillary waves on the turbulent dynamics [18, 30].
The study of 3-wave interactions
between gravity-capillary waves allows us to
validate experimentally, for the first time
for noncolinear waves, the
theory of 3-wave resonant interactions
[24]. We have also obtain
the first indirect measurement of the energy
flux at each scale of the turbulent cascade
[21]. As a consequence,
the highlighting of dissipation at all
scales of the capillary turbulent cascade
(not taken into account in the current stage
of theoretical developments) allowed to
understand the disagreements observed, these
last years, in numerous experiences on
capillary wave turbulence. The constant of the
Kolmogorov-Zakharov spectrum was also
inferred experimentally for the first time
and compared with its theoretical value [21, 23].
Besides, we made the first direct numerical
simulations of capillary wave turbulence
from the two-phase Navier-Stokes equations [22].
These simulations confirm the validity of
weak turbulence derivation when hypotheses
are verified. Finally, we have studied for
the first time wave turbulence on the
interface between two immiscible fluids with
free upper surface. We show that the
coupling between free surface waves and
interface waves modify strongly the wave
turbulence regime [26].
Gravity
wave turbulence: Large scale experiments
Gravity wave turbulence is of primordial interest in oceanography but remains
still not well understood. Beyond the observation of the
direct cascade of gravity wave turbulence, we showed that the
wave spectrum is non-universal and depend on the forcing
parameters [1]. We reported the first
laboratory observations of an inverse cascade of gravity wave
turbulence [15]. Moreover, we experimentally
showed that a spatially homogeneous forcing leads to a good
agreement with theoretical predictions [17],
contrary to previous observations with a localized forcing
with wavemakers.
We
performed experiments in large-scale wave basin (50 m x 30
m x 5 m) at Ecole Centrale Nantes, France, involving 4
French laboratories (MSC/Univ. Paris Diderot, LPS/ENS, SPHINX/CEA
Saclay, LHEEA/Ecole Centrale Nantes). The turbulent wave field
is experimentally found to strongly depend on the basin
boundary conditions (absorbing - beach, or reflecting - wall)
although their statistical and spectral properties are close [23]. We have also studied resonant
interactions between nonlinear waves that are the fundamental
mechanism that transfers energy in wave turbulence. The study
of 4-wave interactions between gravity waves allow us to
validate experimentally, for the first time for noncolinear or
perpendicular waves, the theory of 4-wave resonant
interactions [25]. For stronger
nonlinearities, meaningful departures from this weakly
nonlinear theory are observed [28].
Wave
turbulence in low-gravity environment
We studied purely capillary
waves in low-gravity environment during CNES Parabolic Flight
Campaigns. We have observed capillary wave turbulence on a
broad range of scales usually masked by the gravity wave
regime on Earth [8]. Another advantage is to
have a system with no boundary, the fluid covering all the internal surface of the spherical cell in low-gravity.
Various patterns (hexagons, lines) have thus been observed on
the spherical fluid surface when the forcing is periodic [8]. See
pictures of wave turbulence in space ; See also
pictures of the team in Space
This type of experiment has just been
performed with different forcing conditions and geometry in
the International Space Station (ISS) in 2017 during CNES
Proxima mission of the French astronaut Thomas Pesquet. The
experiment called FLUIDICS (FLUId DynamICs in Space) is
co-funded by CNES and Airbus [31].
Hydroelastic wave turbulence
Hydroelastic
wave turbulence focuses on random waves propagating on
the surface of a fluid covered by an elastic sheet. It
has been obtained for the first time in laboratory [20]. The
existence of three-wave interactions, predicted
theoretically in this system, has just been
highlighted experimentally [27].
Hydroelastic waves, including
gravity-bending waves, are found in various domains:
on the surface of lakes or oceans covered by ice, or
for very large floating structures in oceanography,
flapping flags, or in biomedical applications such as
heart valves.
Magnetic
wave turbulence
We report the first observation
of magnetic wave turbulence on the surface of a
ferrofluid submitted to a magnetic field, a regime
that has not yet been envisaged in theoretical
studies.
When wave amplitudes are high
enough, the wave turbulence theory predicts a
nonlinear resonant process between waves that
generates smaller wavelengths. In a ferrofluid (a
liquid with a suspension of nanometric magnetic
particles), the dispersion relation of surface waves
was known to be tuned by applying a magnetic field.
This leads the authors to the first observation of a
magnetic wave turbulence regime [5]. The existence domains of
gravity and capillary wave turbulence are also
documented as well as a triple point of coexistence of
these three regimes: these new results are understood
using dimensional analysis. Such an experimental
system where the dispersion relation is tuned by the
operator from a non-dispersive to a dispersive system
is thus of primary interest to test the wave
turbulence theory. The case of a magnetic field
parallel to the fluid surface shows several
differences with the normal case. The striking one is
the meaningful broading of the inertial domain of the
magnetic wave turbulence regime [13].
- PUBLICATIONS on wave turbulence and
wave interactions:
34. A.
Cazaubiel, S. Mawet, A. Darras, G. Grojean, J. J. W. A van
Loon, S. Dorbolo & E.
Falcon 2019
submitted to Physical Review Letters (2019)
Hypergravity Wave Turbulence
33. A. Cazaubiel, F. Haudin, E. Falcon &
M. Berhanu 2019
Physical Review
Fluids 4, 074803 (2019)
Forced three-wave
interactions of gravity-capillary surface waves
32. E. Falcon, 2019
Applications in Nonlinear Dynamics (V. In, P.
Longhini, A. Palacios, Eds.), Springer Nature,
Chap. 25, pp. 259 – 266 (2019)
Wave Turbulence: A Set of
Stochastic Nonlinear Waves in Interaction
31. M.
Berhanu, E. Falcon & S. Fauve 2018,
Wave turbulence in
microgravity
Report to COSPAR (World Committee for Space Research),
42th Scientific Assembly, 14-22 July 2018, Pasasena,
USA, CNES Ed., p. 66 - 67 (2018)
30.
M.
Berhanu, E.
Falcon
& L. Deike
2018
Journal
of
Fluid Mechanics
850,
803 (2018)
Turbulence
of capillary
waves forced
by steep
gravity waves
29.
G.
Michel, B.
Semin, A.
Cazaubiel, F.
Haudin, T.
Humbert, S.
Lepot, F.
Bonnefoy, M.
Berhanu &
E. Falcon
2018
Physical Review Fluids 3, 054801 (2018)
Self-similar
gravity wave
spectra
resulting from
the modulation
of bound waves
28.
F. Bonnefoy,
F. Haudin, G.
Michel, B.
Semin, T.
Humbert, S.
Aumaître, M.
Berhanu &
E. Falcon
2017
La
Houille
Blanche 5,
56 (2017)
Experimental
observation of
four-wave
resonant
interactions
in a wave
basin
27. L.
Deike, M. Berhanu & E. Falcon 2017
Physical
Review Fluids 2, 064803
(2017)
Observation of
hydroelastic three-wave interactions
26. B.
Issenmann, C. Laroche & E. Falcon 2016
EPL 116, 64005 (2016)
Wave
turbulence in a two-layer fluid:
coupling between free surface and
interface waves
25. F. Bonnefoy, F. Haudin, G.
Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu & E.
Falcon 2016
Journal of
Fluid Mechanics
(Rapids) 805, R3 (2016)
Observation of resonant
interactions among surface gravity waves
24. F.
Haudin, A. Cazaubiel, L. Deike, T. Jamin, E.
Falcon and M. Berhanu 2016
Phys. Rev. E 93,
043110 (2016)
Experimental study
of three-wave interactions among
capillary-gravity surface waves
23. L. Deike, B. Miquel, P.
Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon
& F. Bonnefoy 2015
Journal
of Fluid Mechanics 781, 196 (2015)
Role of the basin boudary conditions in
gravity wave turbulence
22. L. Deike, D. Fuster, M.
Berhanu, E. Falcon 2014
Physical
Review Letters 112, 234501 (2014)
Direct
numerical simulations of capillary wave turbulence
21.
L. Deike, M.Berhanu & E. Falcon 2014
Energy flux
measurement from the dissipated energy in capillary wave
turbulence
Physical Review E 89, 023003
(2014)
20. L. Deike, J.-C. Bacri & E.
Falcon 2013
Nonlinear waves on
the surface of a fluid covered by an elastic sheet
Journal of
Fluid Mechanics 733, 394 (2013)
19. S.
Aumaître, E.
Falcon
& S. Fauve
2013
Fluctuations
of the Energy Flux in Wave Turbulence
Advances In Wave
Turbulence (Ed. V.
Shrira, S.
Nazarenko, World
Scientific, Chap.
2, pp. 53-72,
2013)
18. M.Berhanu & E.
Falcon 2013
Space-time-resolved
capillary wave turbulence
Physical Review E 89,
033003 (2013)
17. B.
Issenmann & E. Falcon 2013
Gravity wave
turbulence revealed by horizontal vibrations of the
container
Physical Review E 87,
011001(R) (2013)
16. L. Deike, M. Berhanu
& E. Falcon 2012
Decay of capillary wave
turbulence
Physical Review E 85,
066311 (2012)
15. L. Deike,
C.Laroche & E. Falcon 2011
Experimental
study of the inverse cascade in gravity wave turbulence
EPL 96,
34004 (2011)
14. E. Falcon & C.Laroche 2011
Observation
of depth-induced properties in wave turbulence on the
surface of a fluid
EPL 94,
34003 (2011)
13.
S. Dorbolo & E. Falcon
2011
Wave
turbulence on the surface of a ferrofluid in a horizontal
magnetic field
Phys. Rev. E 83,
046303 (2011)
12. E. Herbert, N. Mordant
& E. Falcon 2010
Observation of
the nonlinear dispersion relation and spatial statistics
of wave turbulence on the surface of a fluid
Phys.
Rev.
Lett.
105, 144502 (2010)
11. E. Falcon, S.G. Roux & B.
Audit 2010
Revealing
intermittency in experimental data with steep power
spectra
EPL 90,
50007 (2010)
10. E. Falcon, S.G. Roux & C.
Laroche 2010
On the
origin of intermittency in wave turbulence
EPL 90,
34005 (2010)
9. E.
Falcon 2010
Laboratory experiments on
wave turbulence
Discrete and
Continuous Dynamical Systems - Series B Vol. 13, N°4, 819 - 840 (2010)
8. C. Falcón, E. Falcon, U. Bortolozzo & S.
Fauve 2009
Capillary wave turbulence
on a spherical fluid surface in zero gravity
EPL 86,
14002 (2009)
7. C. Falcón
& E. Falcon 2009
Fluctuations of
energy flux in a simple dissipative out-of-equilibrium
system
Phys. Rev. E 79,
041110 (2009)
6. E. Falcon 2008
Etudes Expérimentales en Turbulence
d'Ondes
Habilitation à Diriger les
Recherches, 244
pages, Université Paris Diderot (2008) (in french)
5. F. Boyer &
E. Falcon 2008
Wave
turbulence on the surface of a ferrofluid in a magnetic
field
Phys. Rev. Lett. 101, 244502 (2008)
4. S. Fauve & E. Falcon 2008,
Gravity-capillary
wave turbulence
Report to COSPAR (World Committee for Space
Research), 37th Scientific Assembly, 13-20 July
2008, Montréal, Canada, CNES Ed., p. 90 - 91 (2008)
3. E. Falcon, S.
Aumaître, C. Falcón, C. Laroche & S.
Fauve 2008
Fluctuations of energy flux
in wave turbulence
Physical
Review Letters 100, 064503 (2008)
2.
E. Falcon, S. Fauve & C. Laroche 2007
Observation of
intermittency in wave turbulence,
Physical
Review Letters 98,
154501 (2007)
1. E. Falcon, C. Laroche &
S. Fauve 2007
Observation of
gravity-capillary wave turbulence,
Physical Review Letters 98,
094503 (2007)