Research interests
Acoustics : acoustic streaming, interaction with moving boundaries
Surface waves : wave turbulence, sloshing, interaction with moving boundaries
Characterization of out-of-equilibrium systems : fluctuation theorems, instabilities on a turbulent background
Passive acoustics is routinely used to characterize flows in hydrodynamics since acoustic waves are scattered by particles in motion and by the vorticity field. Within its range of applicability, it offers simple, robust and low-cost methods for performing quantitative measurements. Similarly, passive acoustics can be applied to investigate the dynamics of surface waves, the interaction between acoustic and surface waves being a subtle combination of diffraction and Doppler shift. One of my research interests is to identify which characteristics of the surface waves can be measured in this way.
Acoustic waves can also drive Eulerian (non-oscillating) flows, as for instance evidenced in this video. The theoretical study of this phenomenon, called acoustic streaming, can be traced back to Rayleigh in the 19th century, and relies on attenuation mechanisms (e.g., on viscosity). It has recently been discovered that in the presence of a inhomogeneous background temperature (or density) field, owing to a nondissipative mechanism, strong streaming flows are driven. With Greg Chini, I characterized these flows theoretically and numerically. Very few experiments of acoustic streaming in such a regime have been performed: well-controlled experiments in micro-gravity or in stably stratified systems would be invaluable for the theory's quantitative assessment. In practice, for instance, in stably stratified media or aboard spacecraft, such streaming flows could be applied to enhance heat fluxes in the absence of natural convection.
Back-and-forth oscillations of a container filled with fluid often result in spilling as the gravest mode gets excited, a well-known phenomenon experienced in everyday life and of particular importance in industry. Our understanding of sloshing is largely restricted to linear response, and the range of validity of this assumption remains unclear: if we were asked if a linear damping correctly describes the oscillations taking place in a cup of coffee, many of us would hesitate before giving an opinion. I carry out experiments to identify and characterize the mechanisms involved in linear and nonlinear sloshing as, for instance, dynamical wetting and resonant interactions.
I am also interested in the statistical study of many interacting (surface) waves. The phenomenology of this so-called wave turbulent regime is similar to the one of hydrodynamic turbulence: energy injected at the forcing scale is transferred to small scales, where it is eventually dissipated by viscosity. Theoretical works predict self-similar spectra analogous to the Kolmorogov's k-5/3 law. However, contrary to hydrodynamic turbulence, these predictions often differ from experimental results: the range of validity of wave turbulence theory is a longstanding open question. I perform experiments to test this theory both in the laboratory, in the Ecole Centrale de Nantes large wave basin and in low-gravity environments (parabolic flights).
Statistical mechanics is most of the time used to characterize systems at equilibrium (for which the distribution functions are known, as for instance the Maxwell-Boltzmann statistics), as well as near equilibrium (for which the distribution functions can be approximated). However, when very far from equilibrium, very few results of statistical mechanics hold. The so-called fluctuation theorem is one of them. It quantifies unusual events, caused by thermal fluctuations, that would be prohibited in the thermodynamic limit and become observable as the size of the system decreases. With Debra Searles (Bernhardt), I investigated how this theorem can be applied in practice for open systems and in the presence of a random force.
Out-of-equilibrium hydrodynamic systems can also undergo instabilities. Well-known examples include the convective Rayleigh-Bénard instability and the Taylor-Couette instability occurring between two rotating cylinders. In the vicinity of such an instability, the dynamics displays several universal features: for instance, the two pitchfork bifurcations mentioned above are both associated with a critical slowing down and to an amplitude proportional to the square root of the distance to the threshold. These behaviors are well experimentally and theoretically documented. Far fewer studies exist on instabilities occurring when a control parameter is varied within the turbulent regime. In addition, theoretical tools are lacking to handle these problems. The drag crisis provides the oldest example of such an instability (the mean drag of a sphere in a turbulent flow suddenly drops for a critical value of the Reynolds number about 105). Some of my work consists in experimentally characterizing such instabilities.