arXiv subjects

Stéphane Perrard

Publications and source records attributed to Stéphane Perrard.

At least 19 recordsLinked to original sources

arXiv2026

Complex Orthogonal Decomposition (C.O.D.) using Python

This work presents the application of the Complex Orthogonal Decomposition (C.O.D.) to a simple spatio-temporal signal. C.O.D. has been introduced rst in the article of B. Feeny, entitled "A Complex Orthogonal Decomposition for Wave Motion Analysis" [1], published in the Journal of Sound and Vibration. The purpose of this signal analysis method is to extract spatial and temporal modes out of a signal. This approach is especially suited to deal with oscillatory signals where phase information is important and where spatial forms are unknown. We provide two theoretical chapters presenting the main mathematical concepts behind C.O.D. and a series of example (with associated Python scripts) to demonstrate the e ciency of the method and some characteristical features.

eess.SP↗

arXiv2026

Tunable Thin Elasto-Drops

We present an experimental method to fabricate centimetric thin elastic capsules with highly uniform thickness and negligible bending stiffness using silicone elastomers. In our experiments, the capsules thickness is tunable at fabrication, while internal pressure and hoop (circumferential) stress are adjustable via hydrostatic inflation once the capsules are filled and immersed in water. Capsules mechanics are probed through hydro-elastic waves generated by weak mechanical perturbations at the capsule interface. By analyzing the surface wave dynamics in the Fourier domain, we extract the in-plane stress and demonstrate that the hydro-elastic waves are exclusively governed by hoop stress. This \reponse{provides a controllable macroscopic analogue of liquid drops} characterised by an effective surface tension, allowing the capsules to be modeled as large-scale ``elasto-drops'' with an inflation and thickness tunable effective surface tension. \reponse{In this limit, bending stiffness is negligible over the experimentally relevant wavelengths, so that the shell dynamics are governed primarily by in-plane tension.} Our work demonstrates that elasto-drops serve as a robust model system for parametric studies of large-scale \reponse{analogues of} liquid drops with experimentally adjustable surface tension.

cond-mat.soft↗

arXiv2026

High-resolution measurement of sea ice mechanical characteristics using Distributed Acoustic Sensing

Sea ice mechanical properties are involved in dynamical processes acting from the scale of meters to several hundred kilometers. The current rapid changes in the state of polar sea ice require a better understanding and modeling of these processes and, therefore, accurate measurements of properties including sea ice thickness, density, Young's modulus and Poisson's ratio. These properties can be measured by tracking the propagation of elastic waves within the ice. Recent technological advances have enabled the use of fiber-optic cables as cost-effective, dense seismic arrays. Once connected to an interrogator unit and mechanically coupled to a medium, here the ice cover, these cables can monitor strain field propagation, using a technique called Distributed Acoustic Sensing (DAS). In this work, we describe the use of such an array of sensors in the coastal ice of the St. Lawrence Estuary, Canada, where a 600 m long optical fiber was deployed across three different morphological sea ice conditions. During hour-long recordings, we measured the propagation of both multi-modal seismic signals generated by active sources and hydro-elastic swell. We computed dispersion curves of active signals and used Continuous Wavelet Transform (CWT) to observe the evolution of swell characteristics in the different ice areas. The dispersion curves were successfully inverted to measure the spatial evolution of ice thickness, and Young's and flexural rigidity in each of these areas. We observed ice thicknesses from 25 cm to 68 cm and Young's modulus values between 4.5 GPa and 5.7 GPa, in good agreement with values derived from collocated geophone arrays and drill hole thickness measurements. DAS systems therefore appear to be effective in evaluating heterogeneous sea ice mechanical properties and thus sea ice formation history and dynamics.

physics.geo-ph↗

arXiv2025

Wave induced fracture of a sea ice analog

We study at the laboratory scale the rupture of thin floating sheets made of a brittle material under a wave-induced mechanical forcing. We show that the rupture occurs where the curvature is maximum and the break-up threshold strongly depends on the wave properties. We observe that the critical stress for fracture depends on the forcing wavelength. Hence our observations are incompatible with a critical stress criterion for fracture. Instead, our measurements can be rationalized as an energy criterion: a fracture propagates when the material surface energy is lower than the released elastic energy, which depends on the forcing geometry. In light of these findings, it may be worthwhile to revisit current numerical models of sea ice fracture by ocean waves.

physics.flu-dyn↗

arXiv2025

Resonance of an object floating within a surface wavefield

We examine the interaction between floating cylindrical objects and surface waves in the gravity regime. Since the impact of resonance phenomena associated with floating bodies, particularly at laboratory scales, remains underexplored, we focus on the influence of the floats' resonance frequency on wave emission. First, we study the response of floating rigid cylinders to external mechanical perturbations. Using an optical reconstruction technique to measure surface wave fields in both space and time, we study the natural resonance frequency of floats with different sizes. The results indicate that the resonance frequency is influenced by the interplay between the cylinder geometry and the solid-to-fluid density ratio. Second, these floating objects are placed in an incoming wave field. These experiments demonstrate that floats diffract incoming waves, while radiating secondary waves that interfere with the incident wavefield. Minimal wave generation is observed at resonance frequencies. These findings can provide insights for elucidating the behavior of larger structures, such as sea ice floes, in natural wave fields.

physics.flu-dyn↗

arXiv2025

Breakup cascade in gas filament

Despite its importance in both geophysical and industrial contexts, the inertial fragmentation of gas filaments has received much less attention than their liquid counterparts. Yet, gas filaments produce the smallest bubble sizes, which drive gas dissolution, critical to ocean-atmosphere exchange such as carbon dioxide and oxygen, as well as marine aerosols emission, serving as nuclei for cloud condensation and ice particle production. Here, we unravel the fundamental physics governing the splitting of a single filament in a model geometry by combining numerical simulations, laboratory experiments and theory. We show that the splitting of a single filament generates a power-law bubble size distribution following $d^{-3/2}$ with $d$ the volume equivalent bubble diameter, suggesting the existence of a self-similar breakup mechanism, absent in liquid ligament fragmentation. We propose a deterministic model, based on the capillary fragmentation of a filament with power-law shape, which quantitatively captures the bubble size distribution. We demonstrate that the filament shape at breakup sets the size distribution of a first generation of bubbles. This distribution is then reproduced at smaller and smaller scales by latter breakups in a self-similar manner. The $d^{-3/2}$-distribution coincides with the size distribution of small bubbles observed in dilute turbulent flow, such as below breaking waves. We argue that the turbulent bubble size distribution observed in nature arises as the superposition of many individual filament splittings. The turbulence nature of the flow only sets the initial conditions of each splitting dynamics, and play no role in the bubble size selection.

physics.flu-dyn↗

arXiv2025

Bubble breakup probability in turbulent flows

Bubbles drive gas and chemical transfers in various industrial and geophysical contexts, in which flows are typically turbulent. As gas and chemical transfers are bubble size dependent, their quantification requires a prediction of bubble breakup. The most common idea, introduced by Kolmogorov and Hinze, is to consider a sharp limit between breaking and non breaking bubbles, given by $\mathrm{We}_c\approx 1$, where the Weber number $\mathrm{We}$ is the ratio between inertial and capillary forces at the bubble scale. Yet, due to the inherent stochasticity of the flow every bubble might in reality break. In this work, we use a stochastic linear model previously developed to infer the breakup probability of bubbles in turbulence as function of both We and the residence time. This allows us to introduce a definition of the critical Weber number accounting for the time spent by bubbles within a turbulent region. We show that bubble breakup is a memoryless process, whose breakup rate varies exponentially with $\mathrm{We}^{-1}$. The linear model successfully reproduces experimental breakup rates from the literature. We show that the stochastic nature of bubble breakup is central when the residence time of bubbles is smaller than ten correlation times of turbulence at the bubble scale: the transition between breaking and non breaking bubbles is smooth and most bubbles can break. For large residence times, the original vision of Kolmogorov and Hinze is recovered.

physics.flu-dyn↗

arXiv2024

Large-Scale Turbulent Pressure Fluctuations Revealed by Ned Kahn's Artwork

We investigate the dynamics of pendulum chains immersed in turbulent boundary layers. We combine laboratory experiments and video analysis of the kinetic facade exhibits by the artist Ned Kahn, composed of large-scale clusters of centimeter-sized plates oscillating freely in the wind. At the laboratory scale, we show that a one-dimensional pendulum chain immersed in a wind tunnel exhibits a wave dispersion relation derived from a Sine-Gordon equation. Under the wind action, the dynamical response is either dominated by a resonance phenomenon, or a linear response to pressure fluctuations. From amateur video analysis on large-scale kinetic facades, we show that the plate oscillation is driven by the same resonant response mechanisms and the apparent wavy pattern corresponds to the most energetic Fourier mode propagating at the advection speed of pressure fluctuations.

physics.flu-dyn↗

arXiv2024

Bubble shape oscillations in a turbulent environment

We investigate bubble deformations in an homogeneous and isotropic turbulent flow by means of direct numerical simulations of a single bubble in turbulence. We examine interface deformations by decomposing the local radius into the spherical harmonics base. We show that the linear dynamics of each mode, (for low Weber number), can be modeled by a forced stochastic linear oscillator. We measure the coefficients of the model directly from the modes' statistics. We find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, dissipation increases by a factor 15 compared to the quiescent case, at $Re_λ= 55$. This enhanced dissipation originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the integration of pressure over the bubble surface, is independent on bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. Eventually, we investigate the pressure modes' statistics in the absence of bubbles and compare them to the effective forcing statistics. We show that both fields share the same pdf, characterized by exponential tails, and a characteristic timescale corresponding to the eddy turnover time at the mode scale.

physics.flu-dyn↗

arXiv2022

Experimental observations and modeling of sub-Hinze bubble production by turbulent bubble break-up

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_\mathrm{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_\mathrm{H}$ (probing up to $d_0 / d_\mathrm{H} = 8.3$), the size distribution of bubbles smaller than $d_\mathrm{H}$ follows $N(d) \propto d^{-3/2}$, with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small ones. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0 / d_\mathrm{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

physics.flu-dyn↗

arXiv2022

Overload wave-memory induces amnesia of a self-propelled particle

Information storage is a key element of autonomous, out-of-equilibrium dynamics, especially for biological and synthetic active matter. In synthetic active matter however, the implementation of internal memory in self-propelled systems is often absent, limiting our understanding of memory-driven dynamics. Recently, a system comprised of a droplet generating its guiding wavefield appeared as a prime candidate for such investigations. Indeed, the wavefield, propelling the droplet, encodes information about the droplet trajectory and the amount of information can be controlled by a single scalar experimental parameter. In this work, we show numerically and experimentally that the accumulation of information in the wavefield induces the loss of time correlations, where the dynamics can then be described by a memory-less process. We rationalize the resulting statistical behaviour by defining an effective temperature for the particle dynamics where the wavefield acts as a thermostat of large dimensions, and by evidencing a minimization principle of the generated wavefield.

cond-mat.soft↗

arXiv2021

Bubble deformation by a turbulent flow

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations, considering a low-density bubble in the high density turbulent flow at various Weber number (the ratio of turbulent and surface tension forces) using the air-water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber number, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.

physics.flu-dyn↗

arXiv2019

Turbulent windprint on a liquid surface

We investigate the effect of a light turbulent wind on a liquid surface, below the onset of wave generation. In that regime, the liquid surface is populated by small disorganised deformations elongated in the streamwise direction. Formally identified recently by Paquier et al. (2015), the deformations that occur below the wave onset were named wrinkles. We provide here a theoretical framework for this wrinkle regime, using the viscous response of a free surface liquid submitted to arbitrary normal and tangential interfacial stresses at its upper boundary. We relate the spatio-temporal spectrum of the surface deformations to that of the applied interfacial pressure and shear stress fluctuations. For that, we evaluate the spatio-temporal statistics of the turbulent forcing using Direct Numerical Simulation of a turbulent air channel flow, assuming no coupling between the air and the liquid flows. Combining theory and numerical simulation, we thus obtain synthetic wrinkles that reproduce previous experimental investigations. We show that the wrinkles are a multi-scale superposition of random wakes generated by the turbulent fluctuations. They result mainly from the nearly isotropic pressure fluctuations generated in the boundary layer, rather than from the elongated shear stress fluctuations. The wrinkle regime described in this paper naturally arises as the viscous-saturated asymptotic of the inviscid growth theory of Phillips (1957). Experiments indicate that the onset of exponential wave growth depends on the liquid viscosity. Our theory suggests that the empirical criterion for the onset is satisfied when the wrinkle amplitude reaches a given fraction of the viscous sublayer thickness. It indicates that the turbulent fluctuations near the onset may play a role in the triggering of exponential wave growth.

physics.flu-dyn↗

arXiv2019

Tunable bimodal explorations of space from memory-driven deterministic dynamics

We present a wave-memory driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a point-like particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wavefield gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes : linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.

cond-mat.stat-mech↗

arXiv2019

Multi-stable free states of an active particle from a coherent memory dynamics

We investigate the dynamics of a deterministic self-propelled particle endowed with coherent memory. We evidence experimentally and numerically that it exhibits several stable free states. The system is composed of a self-propelled drop bouncing on a vibrated liquid driven by the waves it emits at each bounce. This object possesses a propulsion memory resulting from the coherent interference of the waves accumulated along its path. We investigate here the transitory regime of the build-up of the dynamics which leads to velocity modulations. Experiments and numerical simulations enable us to explore unchartered areas of the phase space and reveal the existence of a self-sustained oscillatory regime. Finally, we show the co-existence of several free states. This feature emerges both from the spatio-temporal non-locality of this path memory dynamics as well as the wave nature of the driving mechanism.

cond-mat.soft↗

arXiv2017

Self-propulsion and crossing statistics under random initial conditions

We investigate the crossing of an energy barrier by a self-propelled particle described by a Rayleigh friction term. We reveal the existence of a sharp transition in the external force field whereby the amplitude dramatically increases. This corresponds to a saddle point transition in the velocity flow phase space, as would be expected for any type of repulsive force field. We use this approach to rationalize the results obtained by Eddi \emph{et al.} [\emph{Phys. Rev. Lett.} \textbf{102}, 240401 (2009)] who studied the interaction between a drop propelled by its accompanying wave field and a submarine obstacle. This wave particle entity can overcome potential barrier, suggesting the existence of a "macroscopic tunneling effect". We show that the effect of self-propulsion is sufficiently strong to generate crossing of the high energy barrier. By assuming a random distribution of initial angles, we define a probability distribution to cross the potential barrier that matches with the data of Eddi \emph{et al.}. This probability is similar to the one encountered in statistical physics for Hamiltonian systems \textit{i.e.} a Boltzmann exponential law.

physics.flu-dyn↗

arXiv2016

Build-up of macroscopic eigenstates in a memory-based constrained system

A bouncing drop and its associated accompanying wave forms a walker. Based on previous works, we show in this article that it is possible to formulate a simple theoretical framework for the walker dynamics. It relies on a time scale decomposition corresponding to the effects successively generated when the memory effects increase. While the short time scale effect is simply responsible for the walker's propulsion, the intermediate scale generates spontaneously pivotal structures endowed with angular momentum. At an even larger memory scale, if the walker is spatially confined, the pivots become the building blocks of a self-organization into a global structure. This new theoretical framework is applied in the presence of an external harmonic potential, and reveals the underlying mechanisms leading to the emergence of the macroscopic spatial organization reported by Perrard et al. (2014, Nature Commun. 5, 3219)

physics.flu-dyn↗

arXiv2016

Chaos driven by interfering memory

The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots the dynamics of a particle. Such a system can be implemented by a bouncing drop generating surface waves sustained by a parametric forcing. The motion of the resulting "walker" when confined in a harmonic potential well is generally disordered. Here we show that these trajectories correspond to chaotic regimes characterized by intermittent transitions between a discrete set of states. At any given time, the system is in one of these states characterized by a double quantization of size and angular momentum. A low dimensional intermittency determines their respective probabilities. They thus form an eigenstate basis of decomposition for what would be observed as a superposition of states if all measurements were intrusive.

cond-mat.soft↗