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Experimental studies on wave turbulence (papers by our group)
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 on wave turbulence are funded by ANR Turbonde 2007-2011, ANR Turbulon 2012-2016, ANR Dysturb 2017-2022, and Simons Foundation 2019-2023.
Our projects on wave turbulence are funded by ANR Turbonde 2007-2011, ANR Turbulon 2012-2016, ANR Dysturb 2017-2022, and Simons Foundation 2019-2023.
Gravity-capillary wave turbulence: Laboratory
experiments
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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 SpaceThis experiment was performed with different forcing conditions and geometry onboard the International Space Station (ISS) in 2017 and 2018 during CNES Proxima mission of the French astronaut Thomas Pesquet. The experiment called FLUIDICS (FLUId DynamICs in Space) was co-funded by CNES and Airbus. Main results have been published recently [31,35].
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].
40. E. Kochurin, G. Ricard, N. Zubarev, and E. Falcon 2022