@unpublished{jamin2024experimental,
  title = {Experimental study of three-dimensional turbulence under a free surface},
  author = {Jamin, Timoth{\'e}e and Berhanu, Michael and Falcon, Eric},
  journal = {arXiv preprint arXiv:2310.16188, In press in Physical Review Fluids},
  doi = {10.48550/arXiv.2401.17871},
  file = {JaminPreprint.pdf},
  year = {2024}
}

In many environmental flows, an air-water free surface interacts with a turbulent flow in the water phase. To reproduce this situation, we propose an original experimental setup, which is an evolution of the Randomly Actuated Synthetic Jet Array (RASJA) device used to study turbulence with a low mean flow. By using a central pump connected to jets, we generate a turbulent flow of tunable intensity with good isotropy and horizontal homogeneity. The maximal turbulent Reynolds number of 8800 is significantly larger than in other systems generating turbulence with low mean flow, including RASJA experiments, for which the flow rate per jet cannot be changed. Using our setup, we characterize the modification of the turbulence under the influence of the free surface, which acts typically for depths smaller than the integral length measured in the bulk. We report that the turbulent fluctuations become strongly anisotropic when approaching the free surface. The vertical velocity fluctuations decrease close to the surface whereas the horizontal ones increase as reported in previous theoretical predictions and numerical observations. We also observe a strong enhancement of the amplitude of the temporal and spatial power spectra of the horizontal velocity at large scales, showing the strengthening of these velocity fluctuations near the free surface.

@article{LeLay2024Magneticlevitation,
  title = {Magnetic levitation in the field of a rotating dipole},
  author = {{Le~Lay}, Gr\'egoire and Layani, Sarah and Daerr, Adrian and Berhanu, Michael and Dolbeault, R\'emy and Person, Till and Roussille, Hugo and Taberlet, Nicolas},
  journal = {Physical Review E},
  volume = {110},
  pages = {045003},
  doi = {10.1103/PhysRevE.110.045003},
  file = {LeLayPreprint.pdf},
  year = {2024}
}

It is well known that two permanent magnets of fixed orientation will either always repel or attract one another regardless of the distance between them. However, if one magnet is rotated at sufficient speed, a stable position at a given equilibrium distance can exist for a second free magnet, and the corresponding forces can be sufficient to counteract gravity, leading to a levitation regime. We show that a stable levitation can be obtained when the rotating magnet is tilted from the rotation axis, with no offset in its position. In this regime, the levitating magnet remains centered and its spinning rate remains negligible, while its magnetic moment precesses in synchronization with the driving magnet. We provide a physical explanation of the levitation through a model relying on static dipolar interactions between the two magnets and present experimental results which validate the proposed theory.

@article{saddier2023breaking,
  title = {Breaking of a floating particle raft by water waves},
  author = {Saddier, Louis and Palotai, Ambre and Aksil, Matheo and Tsamados, Michel and Berhanu, Michael},
  journal = {Physical Review Fluids},
  volume = {9},
  pages = {094302},
  doi = {10.1103/PhysRevFluids.9.094302},
  file = {SaddieretalPreprint.pdf},
  year = {2024},
  video1 = {SaddierMovie_S1.mp4},
  video2 = {SaddierMovie_S2.mp4},
  video3 = {SaddierMovie_S3.mp4},
  video4 = {SaddierMovie_S4.mp4},
  video5 = {SaddierMovie_S5.mp4}
}

When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength about 17 cm is very large compared to the thickness of the raft of order 10 microns. For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a timescale long compared to the period of the wave. We characterize the breaking mechanisms. Then we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a notable resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. However, the mechanics of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea ice fractures due to its bending by the waves.

@article{Chaigne2023emergence,
  title = {Emergence of tip singularities in dissolution patterns},
  author = {Chaigne, Martin and Carpy, Sabrina and Mass{\'e}, Marion and Derr, Julien and {Courrech~du~Pont}, Sylvain and Berhanu, Michael},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {120},
  number = {48},
  pages = {e2309379120},
  year = {2023},
  doi = {10.1073/pnas.2309379120},
  file = {DissolutionSingularitiesPreprint2.pdf}
}

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

@article{Chaigne2023dissolution,
  title = {Dissolution-driven propulsion of floating solids},
  author = {Chaigne, Martin and Berhanu, Michael and Kudrolli, Arshad},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {120},
  number = {32},
  pages = {e2301947120},
  year = {2023},
  doi = {10.1073/pnas.2301947120},
  file = {Chaigne2023DissolutionDrivenPropulsionPreprint.pdf},
  video1 = {SIMovieS1.avi},
  video2 = {SIMovieS2.mp4},
  video3 = {SIMovieS3.mp4},
  video4 = {SIMovieS4.mp4},
  video5 = {SIMovieS5.mp4},
  video6 = {SIMovie6.mp4},
  video7 = {SIMovie7.mp4},
  publisher = {National Academie of Sciences}
}

We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.

@article{Berhanu2022wave,
  title = {Wave spectroscopy in a driven granular material},
  author = {Berhanu, Michael and Merminod, Simon and Castillo, Gustavo and Falcon, Eric},
  journal = {Proceedings of the Royal Society A},
  volume = {478},
  number = {2262},
  pages = {20220014},
  year = {2022},
  doi = {10.1098/rspa.2022.0014},
  file = {RSPA_GranularWavesPreprint.pdf},
  publisher = {The Royal Society},
  video1 = {Movie_S1.mp4},
  video2 = {Movie_S2.mp4},
  video3 = {Movie_S3.mp4},
  video4 = {Movie_S4.mp4},
  video5 = {Movie_S5.mp4},
  video7 = {Movie_S6.mp4},
  video8 = {Movie_S8.mp4}
}

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we study fluid-like and crystal-like two-dimensional states in a driven granular material. In our experimental device, a tunable magnetic field induces and controls remote interactions between the granular particles. We use high-speed video recordings to analyse the velocity fluctuations of individual particles in stationary regime. Using statistical averaging, we find that the particles self-organize into collective excitations characterized by dispersion relations in the frequency-wavenumber space. These findings thus reveal that mechanical waves analogous to condensed matter phonons propagate in driven granular media. When the magnetic coupling is weak, the waves are longitudinal, as expected for a fluid-like phase. When the coupling is stronger, both longitudinal and transverse waves propagate, which is typically seen in solid-like phases. We model the dispersion relations using the spatial distribution of particles and their interaction potential. Finally, we infer the elastic parameters of the granular assembly from equivalent sound velocities, thus realizing the spectroscopy of a granular material.

@article{Sharma2022,
  title = {Alcove formation in dissolving cliffs driven by density inversion instability},
  author = {Sharma, Ram Sudhir and Berhanu, Michael and Kudrolli, Arshad},
  journal = {Physics of Fluids},
  volume = {34},
  number = {5},
  pages = {054118},
  year = {2022},
  doi = {10.1063/5.0092331},
  file = {Sharma2022.pdf},
  publisher = {AIP Publishing LLC}
}

We demonstrate conditions that give rise to cave-like features commonly found in dissolving cliffsides with a minimal two-phase physical model. Alcoves that are wider at the top and tapered at the bottom, with sharp-edged ceilings and sloping floors, are shown to develop on vertical solid surfaces dissolving in aqueous solvents. As evident from descending plumes, sufficiently large indentations evolve into alcoves as a result of the faster dissolution of the ceiling due to a solutal Rayleigh–Bénard density inversion instability. In contrast, defects of size below the boundary layer thickness set by the critical Rayleigh number smooth out, leading to stable planar interfaces. The ceiling recession rate and the alcove opening area evolution are shown to be given to first-order by the critical Rayleigh number. By tracking passive tracers in the fluid phase, we show that the alcoves are shaped by the detachment of the boundary layer flow and the appearance of a pinned vortex at the leading edge of the indentations. The attached boundary layer past the developing alcove is then found to lead to rounding of the other sides and the gradual sloping of the floor.

@article{Berhanu2022Fluids,
  title = {Impact of the Dissipation on the Nonlinear Interactions and Turbulence of Gravity-Capillary Waves},
  author = {Berhanu, Michael},
  journal = {Fluids},
  volume = {7},
  number = {4},
  pages = {137},
  year = {2022},
  doi = {10.3390/fluids7040137},
  file = {fluids-07-00137-v3.pdf},
  publisher = {MDPI}
}

Gravity-capillary waves at the water surface are an obvious example illustrating wave propagation in the laboratory, and also nonlinear wave phenomena such as wave interactions or wave turbulence. However, at high-enough frequencies or small scales (i.e., the frequencies typically above 4 Hz or wavelengths below 10 cm), the viscous dissipation cannot be neglected, which complicates experimental, theoretical, and numerical approaches. In this review, we first derive, from the fundamental principles, the features of the gravity-capillary waves. We then discuss the origin and the magnitude of the viscous wave. dissipation in the laboratory and under field conditions. We then show that the significant level of dissipation has important consequences on nonlinear effects involving waves. The nonlinearity level quantified by the wave steepness must be large enough to overcome the viscous dissipation. Specifically, using water as fluid in the field and in the laboratory, nonlinear wave interactions and wave turbulence occur most of the time in a non-weakly nonlinear regime, when the waves are in the capillary or gravity-capillary range

@article{Cazaubiel2021,
  doi = {https://doi.org/10.1103/PhysRevFluids.6.L112601},
  title = {Three-dimensional turbulence generated homogeneously by magnetic particles},
  year = {2021},
  volume = {6},
  number = {11},
  pages = {L112601},
  author = {Cazaubiel, A. and Gorce, J.-B. and Bacri, J.-C. and Berhanu, M. and Laroche, C. and Falcon, E.},
  journal = {Physical Review Fluids},
  file = {Cazaubiel2021PhysRevFluids6L112601.pdf},
  file2 = {Cazaubiel2021_SuppMatSmallScales.pdf}
}

Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g., via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where the fluid is forced in volume, randomly in space and time, using small magnetic particles remotely driven. Such a forcing generates almost no mean flow and is closer to those of direct numerical simulations of isotropic homogeneous turbulence. We compute the energy spectra and structure functions using local and spatiotemporal flow velocity measurements. The energy dissipation rate is also evaluated consistently in five different ways. Our experimental results confirm the stationary, homogeneous, and isotropic features of such turbulence, and, in particular, the Tennekes’ model for which the Tennekes’ constant is experimentally estimated.

@article{Berhanu2021,
  doi = {https://doi.org/10.1063/5.0052305},
  title = {Solutal convection instability caused by dissolution},
  year = {2021},
  volume = {33},
  number = {7},
  pages = {076604},
  author = {Berhanu, Michael and Philippi, Julien and {Courrech~du~Pont}, Sylvain and Derr, Julien},
  journal = {Physics of Fluids},
  file = {solutalconvectioninstabilityBerhanu_POF_Hal.pdf}
}

When a soluble solid body is suddenly put in contact with water, a convection flow can be generated. Once the fluid layer charged into solute is sufficiently dense, this layer becomes unstable under the action of the buoyancy forces. We perform here a linear stability analysis in order to predict the time of appearance of the convection flow, the onset time, and the associated wavelength. As the base state evolves with time due to the solute diffusion, the usual theoretical methods cannot be used. We show that the criterion of marginal instability with a “frozen base state” used for convection in porous media fails for providing the onset parameters in fluid convection. Here, using a modified criterion, i.e., the instability growth rate must be larger than the time evolution of the base state, we find the onset parameters in satisfying agreement with the previous experimental and numerical works. Our results complete our previous numerical work [J. Philippi et al., “Solutal convection induced by dissolution,” Phys. Rev. Fluids 4, 103801 (2019)] in order to determine the conditions for generating a convective flow under the action of dissolution.

@article{Guerin2020,
  author = {Gu\'erin, A. and Derr, J. and {Courrech~du~Pont}, S. and Berhanu, M.},
  title = {Streamwise dissolution patterns created by a flowing water film},
  journal = {Physical Review Letters},
  year = {2020},
  doi = {10.1103/PhysRevLett.125.194502},
  volume = {125},
  number = {19},
  pages = {194502},
  file = {GuerinPhysRevLett2020.pdf},
  file2 = {Supplemental_Guerin2020.pdf}
}

The dissolution of rocks by rainfall commonly generates streamwise parallel channels, yet the occurrence of these natural patterns remains to be understood. Here, we report the emergence in the laboratory of a streamwise dissolution pattern at the surface of an initially flat soluble material, inclined and subjected to a thin runoff water flow. Nearly parallel grooves about 1 mm wide and directed along the main slope spontaneously form. Their width and depth increase continuously with time until their crests emerge and channelize the flow. Our observations may constitute the early stage of the patterns observed in the field.

@article{Opsomer2020,
  doi = {https://doi.org/10.1103/PhysRevE.102.042907},
  title = {Patterns in magnetic granular media at the crossover from two to three dimensions},
  year = {2020},
  volume = {102},
  number = {4},
  pages = {042907},
  author = {Opsomer, E. and Merminod, S. and Schockmel, J. and Vandewalle, N. and Berhanu, M. and Falcon, E.},
  journal = {Physical Review E},
  file = {Opsomer2020_PhysRevE.102.042907.pdf}
}

We perform three-dimensional particle-based simulations of confined, vibrated, and magnetizable beads to study the effect of cell geometry on pattern selection. For quasi-two-dimensional systems, we reproduce previously observed macroscopic patterns such as hexagonal crystals and labyrinthine structures. For systems at the crossover from two to three dimensions, labyrinthine branches shorten and are replaced by triplets of beads forming upright triangles which self-organize into a herringbone pattern. This transition is associated with increases in both translational and orientational orders.

@article{Falcon2020,
  doi = {https://doi.org/10.1103/PhysRevLett.125.134501},
  title = {Saturation of the inverse cascade in surface gravity-wave turbulence},
  year = {2020},
  volume = {125},
  number = {13},
  pages = {134501},
  author = {Falcon, E. and Michel, G. and Prabhudesai, G. and Cazaubiel, A. and Berhanu, M. and Mordant, N. and Aumaitre, S. and Bonnefoy, F.},
  journal = {Physical Review Letters},
  file = {Falcon2020_PhysRevLett.125.134501.pdf},
  file2 = {Falcon2020_SMInverse2_sr.pdf}
}

We report on the observation of surface gravity-wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity-wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-crested waves.

@article{Cohen2020,
  doi = {https://doi.org/10.1103/PhysRevFluids.5.053802},
  title = {Buoyancy-driven dissolution of inclined blocks: Erosion rate and pattern formation},
  year = {2020},
  volume = {5},
  number = {5},
  pages = {053802},
  author = {Cohen, C. and Berhanu, M. and Derr, J. and {Courrech~du~Pont}, S.},
  journal = {Physical Review Fluids},
  file = {Cohen2020_PhysRevFluids.5.053802.pdf},
  file2 = {Cohen2020_DissolutionSuppCorr.pdf},
  video1 = {SaltDissolving.mp4},
  video2 = {CaramelDissolution.avi}
}

The dissolution of a body into quiescent water leads to density stratifications at the interfaces that drive buoyant flows. Where the stratification is unstable, the flow destabilizes into convective solute plumes. By analogy with the Rayleigh-Bénard instability where concentration replaces temperature, this phenomenon is known as the solutal Rayleigh-Bénard instability. Here we report experiments of the dissolution of inclined rectangular blocks made of salt, caramel, or plaster in aqueous solutions of various concentrations. The solute flows along the block while forming plumes before they detach and sink. This flow along the block organizes the emission of plumes within longitudinal parallel stripes with a well-defined millimeter-scale wavelength. The instability of the flow reflects on the concentration field in the boundary layer, which engraves longitudinal grooves onto the block. These grooves interact with the flow and turn into a paving of three-dimensional, cuplike patterns that grow in size and propagate upstream. These bedforms are reminiscent of the scallop bedforms observed on the walls of cave or icebergs. Whereas the block interface is highly dynamical and evolves through time, it remains flat on the global scale and recedes at a stationary rate. We derive scaling laws for the receding velocity and the pattern genesis at the inclined interface that are based on a concentration boundary layerof constant thickness, which is controlled by the flow instability but where neither the patterns nor the flow along the block play any role. We apply these results to the formation of sublimation patterns.

@article{Castillo2020,
  doi = {https://doi.org/10.1103/PhysRevE.101.032903},
  title = {Tuning the distance to equipartition by controlling the collision rate in a driven granular gas experiment},
  year = {2020},
  volume = {101},
  number = {3},
  pages = {032903},
  author = {Castillo, G. and Merminod, S. and Falcon, E. and Berhanu, M.},
  journal = {Physical Review E},
  file = {Castillo2020_PhysRevE.101.032903.pdf}
}

In a granular gas experiment of magnetized particles confined in a thin layer, the rate of dissipative collisions is tuned by adjusting the amplitude of an external magnetic field. The velocity statistics are analyzed using the dynamic and static structure factors of transverse velocity modes. Using the fluctuating hydrodynamics theory, we measure the deviation from kinetic energy equipartition in this out-of-equilibrium system as a function of the dissipative collision rate. When the collision rate is decreased, the distance to equipartition becomes smaller, meaning that the dynamical properties of this granular gas approach by analogy those of a molecular gas in thermal equilibrium.

@article{Berhanu2019,
  doi = {https://doi.org/10.1209/0295-5075/128/34001},
  title = {Capillary wave turbulence experiments in microgravity},
  year = {2019},
  volume = {128},
  number = {3},
  pages = {34001},
  author = {Berhanu, M. and Falcon, E. and Michel, G. and Gissinger, C. and Fauve, S.},
  journal = {EPL (Europhysics Letters)},
  file = {Berhanu_2019_EPL_128_3400.pdf}
}

Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a spherical container partially filled with water and undergoing sinusoidal or random oscillations. The fluctuations of the interface, recorded with two capacitive probes are analyzed by means of the frequency power spectrum of wave elevation. For high enough forcing amplitudes, we report power-law spectra with exponents close to the prediction of weak wave turbulence theory. However, in this experiment the free-surface steepness is not small compared to 1 and thus the investigated regimes correspond to strongly nonlinear wave turbulence.

@article{Philippi2019,
  doi = {https://doi.org/10.1103/PhysRevFluids.4.103801},
  title = {Solutal convection induced by dissolution},
  year = {2019},
  volume = {4},
  number = {10},
  pages = {103801},
  author = {Philippi, J. and Berhanu, Michael and Derr, Julien and {Courrech~du~Pont}, Sylvain},
  journal = {Physical Review Fluids},
  file = {Philippi2019_PhysRevFluids.4.103801.pdf},
  video1 = {Philippi2019_supplemental_video.html}
}

The dissolution of minerals into water becomes significant in geomorphology whenthe erosion rate is controlled by the hydrodynamic transport of the solute. Even in the absence of an external flow, dissolution itself can induce a convective flow due to theaction of gravity. Here we perform a study of the physics of solutal convection induced by dissolution. We simulate numerically the hydrodynamics and the solute transport in atwo-dimensional geometry, corresponding to the case where a soluble body is suddenlyimmersed in a quiescent solvent. We identify three regimes. At a short timescale, a concentrated boundary layer grows by diffusion at the interface. After a finite onset time,the thickness and the density reach critical values, which starts the destabilization ofthe boundary layer. Finally, the destabilization is such that we observe the emission ofintermittent plumes. This last regime is quasistationary: The structure of the boundary layer and the erosion rate fluctuate around constant values. Assuming that the destabilization ofthe boundary layer occurs at a specific value of the solutal Rayleigh number, we derivescaling laws for both fast and slow dissolution kinetics. Our simulations confirm thisscenario by validating the scaling laws for both onset and the quasistationary regime. We find a constant value of the Rayleigh number during the quasistationary regime, showing that the structure of the boundary layer is well controlled by the solutal convection. Weapply the scaling laws previously established to the case of real dissolving minerals. We predict the typical dissolution rate in the presence of solutal convection. Our results suggest that solutal convection could occur in more natural situations than expected. Even for minerals with a quite low saturation concentration, the erosion rate would increase as the dissolution would be controlled by the hydrodynamics.

@article{Cazaubiel2019,
  doi = {https://doi.org/10.1103/PhysRevFluids.4.074803},
  title = {Forced three-wave interactions of capillary-gravity surface waves},
  year = {2019},
  volume = {4},
  number = {7},
  pages = {074803},
  author = {Cazaubiel, Annette and Haudin, Florence and Falcon, Eric and Berhanu, Michael},
  journal = {Physical Review Fluids},
  file = {Cazaubiel_PhysRevFluids.4.074803.pdf}
}

Three-wave resonant interactions constitute an essential nonlinear mechanism couplingcapillary surface waves. In a previous work [Haudin et al. Phys. Rev.E 93, 043110 (2016) ], we characterized experimentally the generation by this mechanism of a daughter wave,whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersionrelation. By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. The bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation. The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with non negligible dissipation.

@article{Berhanu2019up,
  doi = {https://doi.org/10.1103/PhysRevE.99.043102},
  title = {Uplift of an elastic membrane by a viscous flow},
  year = {2019},
  volume = {99},
  number = {4},
  pages = {043102},
  author = {Berhanu, Michael and Guérin, Adrien and {Courrech~du~Pont}, Sylvain and Raoult, Fiona and Perrier, Rémi and Michaut, Chloé},
  journal = {Physical Review E},
  file = {Berhanu2019_PhysRevE.99.043102.pdf}
}

The uplift of an initially flat elastic membrane by an upward viscous flow is investigated experimentally. The deformed shape of the membrane results from a balance between the flow pressure, the elastic response of the membrane, and the fluid weight. This last effect becomes non-negligible for a large enough deformed area. The usual theoretical approach supposes the presence of a prewetting film regularizing the viscous stresses according to Lister et al. [Phys. Rev. Lett. 111, 154501 (2013)]. Nevertheless, in our experiments without prewetting films, the measurements are correctly described with this theory in the elastic regime. Microscale roughness of membranes could introduce an equivalent characteristic scale in the problem. An alternative explanation could be provided by the appearance of a fluid lag filled with gas, for which a new theoretical framework has been recently proposed by Ball and Neufeld [Phys. Rev. Fluids 3, 074101 (2018)]. We compare the two approaches and find that both describe reasonably our experiments. However, consistency tests of both models show that the prewetting film model is more appropriate to describe our experimental data.

@article{Cazaubiel2018,
  doi = {https://doi.org/10.1103/PhysRevFluids.3.114802},
  title = {Coexistence of solitons and extreme events in deep water surface waves},
  year = {2018},
  volume = {3},
  number = {11},
  pages = {114802},
  author = {Cazaubiel, Annette and Michel, Guillaume and Lepot, Simon and Semin, Benoît and Aumaître, Sébastien and Berhanu, Michaël and Bonnefoy, Félicien and Falcon, Eric},
  journal = {Physical Review Fluids},
  file = {Cazaubiel2018_PhysRevFluids.3.114802.pdf}
}

We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave background. Such a coexistence is expected by the integrable turbulence theory for the nonlinear Schrödinger equation (NLSE), and we report the first experimental observation in the context of hydrodynamic waves. We characterize the formation, the properties, and the dynamics of these nonlinear coherent structures (solitons and extreme events) within the incoherent wave background. The extreme events result from the strong steepening of wave train fronts, and their emergence occurs after roughly one nonlinear length scale of propagation (estimated from the NLSE). Solitons arise when nonlinearity and dispersion are weak, and of the same order of magnitude as expected from the NLSE. We characterize the statistical properties of this state. The number of solitons and extreme events is found to increase all along the propagation, the wave-field distribution has a heavy tail, and the surface elevation spectrum is found to scale as a frequency power law with an exponent −4.5±0.5. Most of these observations are compatible with the integrable turbulence theory for the NLSE although some deviations (e.g., power-law spectrum, asymmetrical extreme events) result from effects proper to hydrodynamic waves.

@article{Berhanu2018,
  doi = {https://doi.org/10.1017/jfm.2018.467},
  title = {Turbulence of capillary waves forced by steep gravity wave},
  year = {2018},
  volume = {850},
  pages = {803-804},
  author = {Berhanu, M. and Falcon, E. and Deike, L.},
  journal = {Journal of Fluid Mechanics},
  file = {Berhanu2018_JFM.pdf},
  file2 = {Berhanu2018_JFM_moviedescription.txt},
  video1 = {Berhanu_2018_S0022112018004676sup001.flv},
  video2 = {Berhanu2018_S0022112018004676sup002.flv}
}

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in the laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2–0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from the large scale to the small scale. Analysis of temporal fluctuations of the spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to the small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of the wave spectra are found to be in agreement with those of the weakly nonlinear wave turbulence theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with wave turbulence theory. These results suggest that theoretical developments beyond the classic wave turbulence theory are necessary to describe the dynamics and statistics of capillary waves in a natural environment. In particular, in the presence of broad-scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions should be reconsidered.

@article{Michel2018,
  doi = {https://doi.org/10.1103/PhysRevFluids.3.054801},
  title = {Self-similar gravity wave spectra resulting from the modulation of bound waves},
  year = {2018},
  volume = {3},
  number = {5},
  pages = {054801},
  author = {Michel, Guillaume and Semin, Benoît and Cazaubiel, Annette and Haudin, Florence and Humbert, Thomas and Lepot, Simon and Bonnefoy, Félicien and Berhanu, Michaël and Falcon, Éric},
  journal = {Physical Review Fluids},
  file = {Michel2018_PhysRevFluids.3.054801.pdf}
}

We experimentally study the properties of nonlinear surface gravity waves in a large-scale basin. We consider two different configurations: a one-dimensional (1D) monochromatic wave forcing, and a two-dimensional (2D) forcing with bichromatic waves satisfying resonant-wave interaction conditions. For the 1D forcing, we find a discrete wave-energy spectrum dominated at high frequencies by bound waves whose amplitudes decrease as a power law of the frequency. Bound waves (e.g., to the carrier) are harmonics superimposed on the carrier wave propagating with the same phase velocity as the one of the carrier. When a narrow frequency random modulation is applied to this carrier, the high-frequency part of the wave-energy spectrum becomes continuous with the same frequency-power law. Similar results are found for the 2D forcing when a random modulation is also applied to both carrier waves. Our results thus show that all these nonlinear gravity wave spectra are dominated at high frequencies by the presence of bound waves, even in the configuration where resonant interactions occur. Moreover, in all these configurations, the power-law exponent of the spectrum is found to depend on the forcing amplitude with the same trend as the one found in previous gravity wave turbulence experiments. Such a set of bound waves may thus explain this dependence that was previously poorly understood.

@article{BonnefoyLHB2017,
  doi = {https://doi.org/10.1051/lhb/2017045 },
  title = {Experimental observation of four-wave resonant interactions in a wave basin},
  year = {2017},
  volume = {5},
  pages = {56-63},
  author = {Bonnefoy, F. and Haudin, F. and Michel, G. and Semin, B. and Humbert, T. and Aumaître, S. and Berhanu, M. and Falcon, E.},
  journal = {La Houille Blanche },
  file = {Bonnefoy_LaHouilleBlanche2017.pdf}
}

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepness and directions. These mother waves mutually interact and give birth to a daughter wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results at low steepness are found in good quantitative agreement with four-wave interaction theory [Longuet-Higgins, 1962] with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated. Waves with stronger steepness produce new daughter waves that are explained by means of Zakharov [1968] theory.

@article{Deike2017,
  doi = {https://doi.org/10.1103/PhysRevFluids.2.064803},
  title = {Experimental observation of hydroelastic three-wave interactions},
  year = {2017},
  volume = {2},
  number = {6},
  pages = {064803},
  author = {Deike, Luc and Berhanu, Michael and Falcon, Eric},
  journal = {Physical Review Fluids},
  file = {Deike2017_PhysRevFluids.2.064803.pdf}
}

We study experimentally three-wave interactions between hydroelastic waves propagating on the surface of a fluid covered by an elastic sheet (where both tension and bending are important). We observe the generation of a resonant daughter wave by nonlinear interaction among two mother waves of almost perpendicular directions. By using local and spatiotemporal wave-height measurements, the frequency and wave vector of the daughter wave are found to satisfy the resonance conditions within the measurement accuracy. Its amplitude is also found to be reasonably well described by the resonant wave interaction theory. Finally, a phase-locking among interacting waves is also observed, as expected theoretically.

@article{Cohen2016,
  doi = {https://doi.org/10.1103/PhysRevFluids.1.050508},
  title = {Erosion patterns on dissolving and melting bodie},
  year = {2016},
  volume = {1},
  number = {5},
  pages = {050508},
  author = {Cohen, Caroline and Berhanu, Michael and Derr, Julien and {Courrech~du~Pont}, Sylvain},
  journal = {Physical Review Fluids},
  file = {Cohen2016_PhysRevFluids.1.050508.pdf}
}

This paper is associated with a poster winner of a 2015 APS/DFD Gallery of FluidMotion Award. The original poster is available from the Gallery of Fluid Motion,http://dx.doi.org/10.1103/APS.DFD.2015.GFM.P0051

@article{Bonnefoy2016,
  doi = {https://doi.org/10.1017/jfm.2016.576},
  title = {Experimental observation of four-wave resonant interactions in a wave basin},
  year = {2016},
  volume = {805},
  pages = {R3},
  author = {Bonnefoy, F. and Haudin, F. and Michel, G. and Semin, B. and Humbert, T. and Aumaître, S. and Berhanu, M. and Falcon, E.},
  journal = {Journal of Fluid Mechanics},
  file = {BonnefoyJFM2016_observation-of-resonant-interactions-among-surface-gravity-waves.pdf},
  file2 = {Bonnefoy2016_S0022112016005760sup001.pdf}
}

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated.

@article{Haudin2016,
  doi = {https://dx.doi.org/10.1103/PhysRevE.93.043110},
  title = {Experimental study of three-wave interactions among capillary-gravity surface waves},
  year = {2016},
  volume = {93},
  number = {4},
  pages = {043110},
  author = {Haudin, F. and Cazaubiel, A. and Deike, L. and Jamin, T. and Falcon, E. and Berhanu, Michael},
  journal = {Physical Review E},
  file = {Haudin2016_PhysRevE.pdf}
}

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

@article{Merminod2015,
  doi = {https://doi.org/10.1103/PhysRevE.92.062205},
  title = {Transition to a labyrinthine phase in a driven granular medium},
  year = {2015},
  volume = {92},
  number = {6},
  pages = {062205},
  author = {Merminod, Simon and Jamin, Timothée and Falcon, Eric and Berhanu, Michael},
  journal = {Physical Review E},
  file = {Merminod2015_PhysRevE.92.062205.pdf},
  video = {Merminod2015_Video.mp4}
}

Labyrinthine patterns arise in two-dimensional physical systems submitted to competing interactions, in fields ranging from solid-state physics to hydrodynamics. For systems of interacting particles, labyrinthine and stripe phases were studied in the context of colloidal particles confined into a monolayer, both numerically by means of Monte Carlo simulations and experimentally using superparamagnetic particles. Here we report an experimental observation of a labyrinthine phase in an out-of-equilibrium system constituted of macroscopic particles. Once sufficiently magnetized, they organize into short chains of particles in contact and randomly orientated. We characterize the transition from a granular gas state towards a solid labyrinthine phase, as a function of the ratio of the interaction strength to the kinetic agitation. The spatial local structure is analyzed by means of accurate particle tracking. Moreover, we explain the formation of these chains using a simple model.

@article{Bonnefoy2015,
  doi = {https://doi.org/10.1017/jfm.2015.494},
  title = {Role of the basin boundary conditions in gravity wave turbulence},
  year = {2015},
  volume = {781},
  pages = {196 - 225},
  author = {Deike, Luc and Miquel, Benjamin and Gutiérrez, P. and Jamin, Timothée and Semin, Benoit and Berhanu, Michael and Falcon, Eric and Bonnefoy, Félicien},
  journal = {Journal of Fluid Mechanics},
  file = {Deike2015_role-of-the-basin-boundary-conditions-in-gravity-wave-turbulence.pdf}
}

Gravity wave turbulence is investigated experimentally in a large wave basin in which irregular waves are generated unidirectionally. The roles of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. A quasi-one-dimensional field of nonlinear waves propagates towards the beach, where they are damped whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency power law with an exponent that increases continuously with the forcing amplitude up to a value close to −4 . The physical mechanisms involved most likely differ with the boundary condition used, but cannot be easily discriminated with only temporal measurements. We also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large-scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov–Zakharov constant of the weak turbulence theory is evaluated and found to be compatible with a recently obtained theoretical value.

@article{Jamin2015,
  doi = {https://doi.org/10.1098/rspa.2015.0069},
  title = {Role of the basin boundary conditions in gravity wave turbulence},
  year = {2015},
  volume = {471},
  number = {2178},
  pages = {20150069},
  author = {Jamin, Timothée and Gordillo, Leonardo and Ruiz-Chavarría, Gerardo and Berhanu, Michael and Falcon, Eric},
  journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  file = {JaminGordillo2015_rspa.2015.0069.pdf},
  data = {https://figshare.com/articles/dataset/Experiments_on_tsunami_waves/979238}
}

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

@article{DeikePRL2014,
  author = {Deike, Luc and Fuster, Daniel and Berhanu, Michael and Falcon, Eric},
  title = {Direct Numerical Simulations of Capillary Wave Turbulence},
  journal = {Physical Review Letters},
  year = {2014},
  doi = {https://doi.org/10.1103/PhysRevLett.112.234501},
  volume = {112},
  number = {23},
  pages = {234501},
  file = {Deike2014_PhysRevLett.112.234501.pdf},
  file2 = {Deike2014_DNSCapWT_SM.pdf}
}

This work presents direct numerical simulations of capillary wave turbulence solving the full three-dimensional Navier-Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency, in good agreement with weak turbulence theory. By estimation of the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction, and dissipative times is also observed. These numerical results confirm the validity of the weak turbulence approach to quantify out-of equilibrium wave statistics.

@article{Merminod2014,
  author = {Merminod, S. and Berhanu, M. and Falcon, E.},
  title = {Transition from a dissipative to a quasi-elastic system of particles with tunable repulsive interactions},
  journal = {EPL (Europhysics Letters) },
  year = {2014},
  doi = {10.1209/0295-5075/106/44005},
  volume = {106},
  number = {4},
  pages = {44005},
  file = {Merminod_2014_EPL_106_44005.pdf},
  file2 = {Merminod2014_Moviesdescription.txt},
  video1 = {Merminod2014_Video1.mpg},
  video2 = {Merminod2014_Video2.mpg},
  video3 = {Merminod2014_Video3.mpg},
  video4 = {Merminod2014_Video4.mpg}
}

A two-dimensional system of particles with tunable repulsive interactions is experimentally investigated. Soft ferromagnetic particles are placed on a vibrating rough plate and vertically confined, so that they perform a horizontal Brownian motion in a cell. When immersed in an external vertical magnetic field, the particles become magnetised and thus interact according to a dipolar repulsive law. As the amplitude of the magnetic field is increased, magnetic repulsion raises and the rate of inelastic collisions decreases. Studying notably the pair correlation function and the particle velocity distributions, we show that the typical properties of such a dissipative out-of-equilibrium granular gas are progressively lost, to approach those expected for a usual gas at thermodynamic equilibrium. For stronger interaction strengths, the system gradually solidifies towards a hexagonal crystal. This new setup could consequently be used as a model experimental system for out-of-equilibrium statistical physics, in which the distance to the quasi-elastic limit can be accurately controlled.

@article{DeikePRE2014,
  author = {Deike, Luc and Berhanu, Michael and Falcon, Eric},
  title = {Energy flux measurement from the dissipated energy in capillary wave turbulence},
  journal = {Physical Review E},
  year = {2014},
  doi = {10.1103/PhysRevE.89.023003},
  volume = {89},
  number = {2},
  pages = {023003},
  file = {Deike2014_PhysRevE.89.023003.pdf}
}

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

@article{BerhanuPRE2013,
  author = {Berhanu, Michael and Falcon, Eric},
  title = {Space-time-resolved capillary wave turbulence},
  journal = {Physical Review E},
  year = {2013},
  doi = {http://dx.doi.org/10.1103/PhysRevE.87.033003},
  volume = {87},
  number = {3},
  pages = {033003},
  file = {Berhanu2013_PhysRevE.87.033003.pdf},
  file2 = {Berhanu2013_supplemental.pdf},
  movie1 = {Berhanu2013_WaveFieldHigh.mpg},
  movie2 = {Berhanu2013_WaveSteepnessHigh.mpg},
  movie3 = {Berhanu2013_WaveFieldLow.mpg},
  movie4 = {Berhanu2013_WaveSteepnessLow.mpg}
}

We report experiments on the full space- and time-resolved statistics of capillary wave turbulence at the air-water interface. The three-dimensional shape of the free interface is measured as a function of time by using the optical method of diffusing light photography associated with a fast camera. Linear and nonlinear dispersion relations are extracted from the spatiotemporal power spectrum of wave amplitude. When wave turbulence regime is reached, we observe power-law spectra both in frequency and in wave number whose exponents are found to agree with the predictions of capillary wave turbulence theory. Finally, the temporal dynamics of the spatial energy spectrum highlight the occurrence of stochastic bursts transferring wave energy through the spatial scales.

@article{BerhanuPRE2014,
  author = {Dasgupta, Moumita and Liu, Bin and Fu, Henry C. and Berhanu, Michael and Breuer, Kenneth S. and Powers, Thomas R. and Kudrolli, Arshad},
  title = {Speed of a swimming sheet in Newtonian and viscoelastic fluids},
  journal = {Physical Review E},
  year = {2013},
  doi = {10.1103/PhysRevE.87.013015},
  volume = {87},
  number = {1},
  pages = {013015},
  file = {Dasgupta2013_PhysRevE.87.013015.pdf}
}

We measure the swimming speed of a cylindrical version of Taylor’s swimming sheet in viscoelastic fluids, and find that depending on the rheology, the speed can either increase or decrease relative to the speed in a Newtonian viscous fluid. The swimming stroke of the sheet is a prescribed propagating wave that travels along the sheet in the azimuthal direction. The measurements are performed with the sheet immersed in a fluid inside a cylindrical tank under torque-free conditions. Swimming speeds in the Newtonian case are found to be consistent with calculations using the Stokes equation. A faster swimming speed is found in a viscoelastic fluid that has a viscosity independent of shear rate. By contrast, a slower swimming speed is found with more complex shear-thinning viscoelastic fluids which have multiple relaxation time scales as well. These results are compared with calculations with Oldroyd-B fluids which find a decreasing swimming speed with Deborah number given by the product of the fluid elastic relaxation time scale and the driving frequency.

@article{BerhanuPRE2012,
  author = {Berhanu, Michael and Petroff, Alexander and Devauchelle, Olivier and Kudrolli, Arshad and Rothman, Daniel H.},
  title = {Shape and dynamics of seepage erosion in a horizontal granular bed},
  journal = {Physical Review E},
  year = {2012},
  doi = {10.1103/PhysRevE.86.041304},
  volume = {86},
  number = {4},
  pages = {041304},
  file = {Berhanu2012_PhysRevE.86.041304.pdf}
}

We investigate erosion patterns observed in a horizontal granular bed resulting from seepage of water motivated by observation of beach rills and channel growth in larger scale land forms. Our experimental apparatus consists of a wide rectangular box filled with glass beads with a narrow opening in one of the side walls from which eroded grains can exit. Quantitative data on the shape of the pattern and erosion dynamics are obtained with a laser-aided topography technique. We show that the spatial distribution of the source of groundwater can significantly impact the shape of observed patterns. An elongated channel is observed to grow upstream when groundwater is injected at a boundary adjacent to a reservoir held at constant height. An amphitheater (semicircular) shape is observed when uniform rainfall infiltrates the granular bed to maintain a water table. Bifurcations are observed as the channels grow in response to the groundwater. We further find that the channels grow by discrete avalanches as the height of the granular bed is increased above the capillary rise, causing the deeper channels to have rougher fronts. The spatiotemporal distribution of avalanches increase with bed height when partial saturation of the bed leads to cohesion between grains. However, the overall shape of the channels is observed to remain unaffected indicating that seepage erosion is robust to perturbation of the erosion front.

@article{DeikePRE2012,
  author = {Deike, Luc and Berhanu, Michael and Falcon, Eric},
  title = {Decay of capillary wave turbulence},
  journal = {Physical Review E},
  year = {2012},
  doi = {10.1103/PhysRevE.85.066311},
  volume = {85},
  number = {6},
  pages = {066311},
  file = {Deike2012_PhysRevE.85.066311.pdf}
}

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by a viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.

@article{DalbePRE2011,
  author = {Dalbe, Marie-Julie and Cosic, Darija and Berhanu, Michael and Kudrolli, Arshad},
  title = {Aggregation of frictional particles due to capillary attraction},
  journal = {Physical Review E},
  year = {2012},
  doi = {10.1103/PhysRevE.83.051403},
  volume = {83},
  number = {5},
  pages = {051403},
  file = {Dalbe2012_PhysRevE.83.051403.pdf}
}

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster—the lowest-energy state—depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.

@article{BerhanuEPJB2010,
  author = {Berhanu, M. and Verhille, G. and Boisson, J. and Gallet, B. and Gissinger, C. and Fauve, S. and Mordant, N. and Pétrélis, F. and Bourgoin, M. and Odier, P. and Pinton, J.-F. and Plihon, N. and Aumaître, S. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Pirat, C.},
  title = {Dynamo regimes and transitions in the VKS experiment},
  journal = {The European Physical Journal B},
  year = {2010},
  doi = {http://dx.doi.org/10.1140/epjb/e2010-00272-5},
  volume = {77},
  number = {9},
  pages = {459-468},
  file = {Berhanu2010_Article_DynamoRegimesAndTransitionsInT.pdf}
}

The Von Kármán Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F 1 and F 2. We show that as the intensity of forcing, measured as F 1+F 2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter θ = (F 1–F 2)/(F 1+F 2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes. 

@article{BerhanuPRL2010,
  author = {Berhanu, Michael and Kudrolli, Arshad},
  title = {Heterogeneous Structure of Granular Aggregates with Capillary Interactions},
  journal = {Physical Review Letters},
  year = {2010},
  doi = {http://dx.doi.org/10.1103/PhysRevLett.105.098002},
  volume = {105},
  number = {9},
  pages = {098002},
  file = {Berhanu2010_PhysRevLett.105.098002.pdf},
  file2 = {Berhanu2010_suppl.pdf},
  file3 = {Berhanu2010_Moviesdescription.txt},
  movie1 = {Berhanu2010_movie1.mpg},
  movie2 = {Berhanu2010_movie2.mpg},
  movie3 = {Berhanu2010_movie3.mpg}
}

We investigate the spatial structure of cohesive granular matter with spheres floating at an air-liquid interface that form disordered close packings with pores in between. The interface is slowly lowered in a conical container to uniformly compress and study the system as a function of area fraction ϕ. We find that the free area distributions associated with Voronoi cells show significant exponential tails indicating greater heterogeneity compared with random distributions at low ϕ with a crossover towards a Γ distribution as ϕ is increased. Further, we find significant short range order as measured by the radial correlation function and the orientational order parameter even at low and intermediate ϕ, which is absent when particles interact only sterically.

@article{BerhanuJFM2009,
  author = {Berhanu, M. and Gallet, B. and Monchaux, R. and Bourgoin, M. and Odier, P. and Pinton, J.-F. and Plihon, N. and Volk, R. and Fauve, S. and Mordant, N. and Pétrélis, F. and Aumaître, S. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Ravelet, F.},
  title = {Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium},
  journal = {Journal of Fluid Mechanics},
  year = {2009},
  doi = {10.1017/S0022112009991996},
  volume = {641},
  pages = {217-226},
  file = {BerhanuJFM2009_bistability-between-a-stationary-and-an-oscillatory-dynamo-in-a-turbulent-flow-of-liquid-sodium.pdf}
}

We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Kármán geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

@article{GalletPOF2009,
  author = {Gallet, B. and Berhanu, M. and Mordant, N.},
  title = {Influence of an external magnetic field on forced turbulence in a swirling flow of liquid metal},
  journal = {Physics of Fluids},
  year = {2009},
  doi = {10.1063/1.3194304},
  volume = {21},
  number = {8},
  pages = {085107},
  file = {Gallet2009_POF.pdf}
}

We report an experimental investigation on the influence of an external magnetic field on forced three-dimensional turbulence of liquid gallium in a closed vessel. We observe an exponential damping of the turbulent velocity fluctuations as a function of the interaction parameter N (ratio of Lorentz force over inertial terms of the Navier–Stokes equation). The flow structures develop some anisotropy but do not become bidimensional. From a dynamical viewpoint, the damping first occurs homogeneously over the whole spectrum of frequencies. For larger values of N, a very strong additional damping occurs at the highest frequencies. However, the injected mechanical power remains independent of the applied magnetic field. The simultaneous measurement of induced magnetic field and electrical potential differences shows a very weak correlation between magnetic field and velocity fluctuations. The observed reduction in the fluctuations is in agreement with a previously proposed mechanism for the saturation of turbulent dynamos and with the order of magnitude of the Von Kármán sodium dynamo magnetic field

@article{MonchauxPOF2009,
  author = {Monchaux, Romain and Berhanu, Michael and Aumaître, Sébastien and Chiffaudel, Arnaud and Daviaud, François and Dubrulle, Bérengère and Ravelet, Florent and Fauve, Stephan and Mordant, Nicolas and Pétrélis, François and Bourgoin, Mickael and Odier, Philippe and Pinton, Jean-Francois and Plihon, Nicolas and Volk, Romain},
  title = {The von Kármán sodium experiment: turbulent dynamical dynamos},
  journal = {Physics of Fluids},
  year = {2009},
  doi = {10.1063/1.3085724},
  volume = {21},
  number = {3},
  pages = {035108},
  file = {Monchaux2009_pof.pdf}
}

The von Kármán Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Kármán geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is Rπ-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

@article{AumaitreCRPhys2008,
  author = {Aumaître, Sébastien and Berhanu, Michael and Bourgoin, Mickael and Chiffaude, Arnaud and Daviaud, François and Dubrulle, Bérengère and Fauve, Stephan and Marié, Louis and Monchaux, Romain and Mordant, Nicolas and Odier, Philippe and Pétrélis, François and Pinton, Jean-François and Plihon, Nicolas and Ravelet, Florent and Volk, Romain},
  title = {The VKS experiment: turbulent dynamical dynamos},
  journal = {Comptes Rendus de l'Académie des sciences, Physique},
  year = {2008},
  doi = {https://doi.org/10.1016/j.crhy.2008.07.002},
  volume = {9},
  number = {7},
  pages = {689-701},
  file = {Aumaitre2008_1-s2.0-S1631070508000959-main.pdf}
}

The VKS experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Kármán geometry). We report observations related to the self-generation of a stationary dynamo when the flow forcing is symmetric, i.e. when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical, with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is asymmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

@article{RaveletPRL2008,
  author = {Ravelet, F. and Berhanu, M. and Monchaux, R. and Aumaître, S. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Bourgoin, M. and Odier, Ph. and Plihon, N. and Pinton, J.-F. and Volk, R. and Fauve, S. and Mordant, N. and Pétrélis, F.},
  title = {Chaotic Dynamos Generated by a Turbulent Flow of Liquid Sodium},
  journal = {Physical Review Letters},
  year = {2008},
  doi = {10.1103/PhysRevLett.101.074502},
  volume = {101},
  number = {7},
  pages = {074502},
  file = {Ravelet2008_PhysRevLett.101.074502.pdf}
}

We report the observation of several dynamical regimes of the magnetic field generated by a turbulent flow of liquid sodium (VKS experiment). Stationary dynamos, transitions to relaxation cycles or to intermittent bursts, and random field reversals occur in a fairly small range of parameters. Large scale dynamics of the magnetic field result from the interactions of a few modes. The low dimensional nature of these dynamics is not smeared out by the very strong turbulent fluctuations of the flow.

@article{BerhanuPRE2008,
  author = {Berhanu, Michael and Gallet, Basile and Mordant, Nicolas and Fauve, Stéphan},
  title = {Reduction of velocity fluctuations in a turbulent flow of gallium by an external magnetic field},
  journal = {Physical Review E},
  year = {2008},
  doi = {10.1103/PhysRevE.78.015302},
  volume = {78},
  number = {1},
  pages = {015302(R)},
  file = {Berhanu2008_PhysRevE.78.015302.pdf}
}

The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe a reduction of velocity fluctuations at all frequencies in the spectrum when the magnetic field is increased.

@article{BerhanuEPL2007,
  author = {Berhanu, M. and Monchaux, R. and Fauve, S. and Mordant, N. and Pétrélis, F. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Marié, L. and Ravelet, F. and Bourgoin, M. and Odier, Ph. and Pinton, J.-F. and Volk, R.},
  title = {Magnetic field reversals in an experimental turbulent dynamo},
  journal = {EPL (Europhysics Letters)},
  year = {2007},
  doi = {10.1209/0295-5075/77/59001},
  volume = {77},
  number = {5},
  pages = {59001},
  file = {Berhanu_2007_EPL_77_59001.pdf}
}

We report the first experimental observation of reversals of a dynamo field generated in a laboratory experiment based on a turbulent flow of liquid sodium. The magnetic field randomly switches between two symmetric solutions B and–B. We observe a hierarchy of time scales similar to the Earth’s magnetic field: the duration of the steady phases is widely distributed, but is always much longer than the time needed to switch polarity. In addition to reversals we report excursions. Both coincide with minima of the mechanical power driving the flow. Small changes in the flow driving parameters also reveal a large variety of dynamo regimes.

@article{MonchauxPRL2007,
  author = {Monchaux, R. and Berhanu, M. and Bourgoin, M. and Moulin, M. and Odier, Ph. and Pinton, J.-F. and Volk, R. and Fauve, S. and Mordant, N. and Pétrélis, F. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Gasquet, C. and Marié, L. and Ravelet, F.},
  title = {Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium},
  journal = {Physical Review Letters},
  year = {2008},
  doi = {10.1103/PhysRevLett.98.044502},
  volume = {98},
  number = {4},
  pages = {044502},
  file = {Monchaux2008_PhysRevLett.98.044502.pdf}
}

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number Rm∼30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

@article{VolkPRL2006,
  author = {Volk, R. and Ravelet, F. and Monchaux, R. and Berhanu, M. and Chiffaudel, A. and Daviaud, F. and Odier, Ph. and Pinton, J.-F. and Fauve, S. and Mordant, N. and Pétrélis, F.},
  title = {Transport of magnetic field by a turbulent flow of liquid sodium},
  journal = {Physical Review Letters},
  year = {2006},
  doi = {10.1103/PhysRevLett.97.074501},
  volume = {97},
  number = {7},
  pages = {074501},
  file = {Volk2006_PhysRevLett.97.074501.pdf}
}

We study the effect of a turbulent flow of liquid sodium generated in the von Kármán geometry, on the localized field of a magnet placed close to the frontier of the flow. We observe that the field can be transported by the flow on distances larger than its integral length scale. In the most turbulent configurations, the mean value of the field advected at large distance vanishes. However, the rms value of the fluctuations increases linearly with the magnetic Reynolds number. The advected field is strongly intermittent.

@inproceedings{BerhanuCospar2018,
  author = {Berhanu, M. and Falcon, E. and Fauve, S.},
  title = {Wave turbulence in microgravity},
  booktitle = {French Report to COSPAR (World Committee for Space Research). 42nd Scientific Assembly},
  year = {2018},
  file = {st_cospar_2018_completv2.pdf}
}

We report experiments conducted by the ESA astronauts T. Pesquet and P. Nespoli on the International Space Station in 2017. Using a new device, “FLUIDICS” (Fluid Dynamics in Space), developed by CNES and Airbus Defence and Space, they studied turbulence of capillary waves on the surface of a fluid in a spherical container. Power spectra of wave turbulence have been found to be in good agreement with weak turbulence theory.

@inproceedings{MignotIAC_2017,
  author = {Mignot, Jean and Pierre, R. and Berhanu, M. and Busset, B. and Roumiguié, R. and Bavestrello, H. and Bonfanti, S. and Miquel, T. and Marot, L.-O. and Llodra-Perez, A.},
  title = {Fluid dynamic in space experiment},
  booktitle = {68th International Astronautical Congress (IAC), Adelaide, Australia (IAC-17-A2. 62)},
  year = {2017},
  file = {IAC-2017-final-Fluidics.pdf}
}

Sloshing phenomena of satellite fuel has become over the last few years a significant disturbance especially for manoeuvring spacecraft with tight performance requirements to ensure. As sloshing can be observed only in 0g domain where capillary forces start dominating the inertial effect, satellite design is mainly based on more or less complex models. Because of the unavailability or inaccessibility of experimental data, these models are often not thoroughly validated.
FLUIDICS (FLUId DynamICs in Space) was a part of the PROXIMA project development during the flight of Thomas Pesquet. The development has been done in close cooperation and funding of Airbus and CNES. The main goal of the experiment is to enable model validation through correlation with measurements. FLUIDICS apparatus is built as a slow rate centrifuge that can establish specific controlled micro-gravity conditions or dedicated excitations on a sample tank. Two cameras offer video recording capability and a dedicated sensor monitors the forces generated by the fluid motion.
For the sloshing part, experimental motion profiles implements several acceleration and speed representative of typical satellite slew manoeuvres and tranquilization phases. Two tanks will be used to study the impact of the filling ratio, representative of the depletion during the satellite lifetime.
The Wave turbulence part uses periodic excitation of small amplitude at different levels and frequencies.
Fluidics experiment is still on-board of Columbus ready to be used in the next few months. Innovative perspectives are also foreseen to study new tanks design mitigating the sloshing impact that can be used on the same FLUIDICS setup.

@inproceedings{BonnefoyReport2017,
  author = {Bonnefoy, F. and Haudin, F. and Michel, G. and Semin, B. and Humbert, T. and Aumaître, S. and Berhanu, M. and Falcon, E.},
  title = {Experimental observation of four-wave resonant interaction: from low steepness to wave breaking},
  booktitle = {Proceedings of the 32nd International Workshop on Water Waves and Floating Bodies},
  year = {2017},
  file = {Bonnefoy2017_170216_1330574.pdf}
}

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant daughter wave whose properties (growth rate, resonant response curve and phase locking) have been fully characterized in Bonnefoy et al.(2016) at low steepness. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. Waves with stronger steepness produce new daughter waves that are measured and explained by means of Zakharov theory. Resulting oblique wave packets are observed which are explained as the interference between these daughter waves generated in a cascade by the four-wave interactions.

@thesis{Berhanu_thesis,
  author = {Berhanu, M.},
  title = {Turbulent magnetohydrodynamics in liquid metals},
  year = {2008},
  school = {Ecole Normale Supérieure, Université Pierre et Marie Curie.},
  note = {Ph.D. Thesis},
  file = {BerhanuThese3.pdf}
}

Manuscript in French. In electrically conducting fluids, the electromagnetic field is coupled with the fluid motion byinduction effects. We studied different magnétohydrodynamic phenomena, using two experiments involving turbulent flows of liquid metal. The first mid-sized uses gallium. The second, using sodium, is conducted within the VKS (Von Karman Sodium) collaboration. It has led to the observation of the dynamo effect, namely converting a part of the kinetic energy of the fluid into magnetic energy. We have shown that, depending on forcing conditions, a statistically stationary dynamo, or dynamical regimes of magnetic field can be generated. In particular, polarity reversals similar to those of Earth’s magnetic field were observed. Meanwhile, experiment with Gallium has been developed to study the effects of electromagnetic induction by turbulent flows in a more homogeneous and isotropic configuration than in the VKS experiment. Using data from these two experiments, we studied the advection of magnetic field by a turbulent flow and the induced fluctuations. The development of probes measuring electrical potential difference allowed us to further highlight the magnetic braking of a turbulent flow of Gallium by Lorentz force. This mechanism is involved in the saturation of the dynamo instability.

@thesis{Berhanu_master,
  author = {Berhanu, M.},
  title = {Hydrodynamique dans un cylindre d'un écoulement généré par deux hélices décentrées.},
  year = {2005},
  school = {Ecole Normale Supérieure },
  note = {Ens Lyon Master thesis},
  file = {M2rapportBerhanu.pdf}
}

In french.