This project aims at developing a theory on the evolution of an initially axisymmetric rotating flow containing conical inertial waves that emerge from a vibrating torus and meet in a focal point. The understanding of this archetypal flow raises several questions pertaining to its topology and dynamics. We will address these questions by combining symmetry group theory and numerical simulations, progressing from the simpler linear model to the more complex turbulent one. First, the symmetry properties of the flow will be exhaustively understood for low forcing amplitudes for which linear wave propagation occurs. Then, this will permit to tackle the weakly nonlinear regime at increasing wave amplitude, where a local shock-like phenomenon occurs at the focal point of the inertial waves. This triggers complex energy transfers between waves but also a yet to be explained transfer to large-scale motion. The analytic basis will be an equation derived from the Euler equation using singular asymptotics in the limit of high rotation rates and valid for large wave amplitudes. The structural symmetry breaking will be explained by a combination of stability theory and group theory, which we plan to relate to dynamical arguments drawn from a statistical analysis of triadic interactions of inertial waves. In addition to this system approach, we will study local phenomena, such as the mechanism limiting the core of non-linearity to a localized region in the flow. After the comprehensive study of the wave-turbulence regime, we will consider the fully turbulent regime in which nonlinearities are strong so that transfers in the flow are mediated by both inertial waves exchanges and by classical turbulent ones, thus producing more complex couplings. Our original approach will be to perform the symmetry analysis of two-point statistical equations, and to relate this to the isotropy-breaking in Direct Numerical Simulations with and without helicity. In the helical case, additional invariants have to be considered. The role of the specific geometry will also be evaluated by a parametric investigation of the cone-shaped inertial waves with and without confinement, also by Direct Numerical Simulations. The most original aspect of our project is thus to integrate in a single study a new theory based on the symmetries of rotating turbulent flows, and a dynamical point of view for anisotropic transfers between scales.

Aquatic ecosystems constitute a topic of high relevance due to their abundance and their various roles on different scales, ranging from the quality of drinking water taken from the local river to the large-scale impact on climate change. The fluid mechanical interaction between the flow and the flexible plants in an aquatic canopy determines hydraulics as well as transport of sediment, nutrients and pollutants. While canopies with rigid elements have been investigated in many laboratory studies, far less is known about canopies with very flexible blades, i.e. high Cauchy number. This lack of knowledge is addressed in the project by a judicious combination of simulations and experiments to investigate their hydromechanics in the presence of reconfiguration and their impact on the transport of scalar quantities. A key feature is the tight connection to ecologically-relevant conditions by involving a specialist for aquatic plants and ecohydraulics. Experiments and simulations are performed for three types of configurations: (1) test configurations of a single blade and a small number of blades to develop and validate methods, (2) homogeneous canopies with uniform blades of high flexibility, (3) canopies with clearances mimicking patch-scale issues. Data for characterization of real, blade-like, aquatic plants and patches are gathered by the ecohydraulics specialist ensuring an optimal choice of parameters for the fluid mechanics experiments and simulations conducted. These partly address exactly the same configuration with, e.g., simulations providing data which cannot be measured. In addition, the respective advantages of experiments and simulations are exploited by performing complementary variations of parameters. This yields a very sound and large database. In both, experiment and simulation, innovative technologies are employed. For the experiments, PIV, PLIF and ADVP are adapted for simultaneous measurements of scalar concentration, fluid velocity and instantaneous position of blades. In particular, the Acoustic Doppler Velocity Profile sensor has not yet been used for this task before. It allows measuring instantaneous velocity profiles both above and inside the canopy simultaneously with blade motion. Convincing simulations of canopies made of flexible elements do not exist up to now. Here, an innovative method is employed combining a highly efficient immersed boundary method with an own semi-implicit coupling algorithm and an extremely efficient scheme for a Cosserat rod. In this way, highly resolved simulations for canopies with thousands of blades are possible furnishing a huge wealth of data. The collaborative assessment of these data, also involving the ecohydraulics specialist, provides an ideal combination of interdisciplinary knowledge. The vision is to generate detailed understanding of the complex processes in and over high-Cauchy number canopies and to turn that into information relevant for aquatic ecosystems.

Dispersed two-phase flows occur in many industrial applications and natural phenomena. In the past decade, significant progress has been achieved in this field, due both to a revolution in experimental techniques (PIV, PLIF, PTV…) and to the extraordinary development of numerical simulations. Interestingly, this domain has been tackled by different scientific communities, in Fluid Mechanics, Physics, Meteorology, or Geophysics, with different focuses and different methods. The case of inertial particles is an emblematic example, with the development of efficient Eulerian or Lagrangian models in Engineering, associated with deep insights in the dynamics of particle-turbulence interaction by physicists studying turbulence, which helped to improve current models. The participants to this project were involved in this global effort and mixing of scientific cultures in a previous ANR program DSPET, devoted to inertial particles. The case of dispersed flows involving mass transfer, due to evaporation, condensation, or dissolution or coalescence is even more intricate, due to the dependence in time of the size of the particulates (drops, bubbles, and particles), which precludes some convenient approximations such as point-particles and one-way coupling. Among the many fundamental difficulties of the problem, the present project objective is to focus on the interaction between turbulence and phase change in particulate flows. Although the specific features of flows with either drops, bubbles or particles make it unlikely that all situations can be described by a single general framework, we believe that common physical principles can be identified in all cases, and that much can be understood with the newly developed experimental and numerical tools. Since the problem is clearly multiscale, the project involves three steps corresponding (i) to a local study at the scale of the particles (Bubble, drop or solid particle), (ii) to the intermediate level (mesoscale) of a swarm of interacting inclusions, basically through turbulent induced collisions, (iii) to the macroscopic level of mean field equations used in applications. Although several aspects of the problem have been investigated, other important aspects, such ascrossing trajectories effects and preferential concentration, or finite size effects on mass transfer and forces, have received little attention until recently. The goal of this proposal is to take advantage of recent advances in the investigation of this long-standing problem, by using the latest available techniques, and a strong coupling between experiments, simulations and modeling. The challenge is to determine both the evaporation/condensation rate along the trajectories, and the local characteristics of the continuous phase in the vicinity of the particle. Experimental techniques developed in the previous ANR program DSPET by the same group (high-speed PTV, high-speed holography, PIV+PLIF) appear to be well adapted for this purpose. Numerical methods accounting for severe evaporation conditions will also been developed. In a second methodological step, we shall consider situations involving many condensing/evaporating bubbles or drops. In such situations, phase changes can be greatly modified by two classes of mechanisms: collisions and coalescence processes, and collective effects. The first one involves essentially binary collisions between particulates, which are affected in a still incompletely understood way by turbulence. The four teams involved in the project, at the LMFA, the Physics Laboratory at ENS Lyon, the LEGI and the OCA, gather some unique competences in advanced measuring techniques and theoretical and numerical modeling. They have a strong experience of common projects, and use to share experimental equipments and numerical codes.

Interest in bubble-induced shear stress is motivated by a variety of technological, chemical, and biomedical applications where this effect is used. Often acoustic cavitation bubbles are involved, and ultrasonic cleaning, micromixing of liquids, intensification of chemical reactions, or heat-exchange processes are examples of such applications in the engineering field. In the biomedical field, ultrasound-mediated drug delivery, ultrasound-induced blood-brain barrier opening, bacteria lysis, or disinfection are examples of bubble-mediated bioeffects. During decades research works mainly focused on the violent mechanisms resulting from cavitation bubble collapses, including shockwave emissions and the generation of microjets. Recent sensitive applications have demonstrated that more weakly oscillating bubbles may also produce significant mechanical effects on rigid or elastic surfaces through the generation of shear stress. This shear stress results from the liquid flows created in vicinity of the oscillating bubbles. Up to now, the influence and modification of surfaces by bubble-induced shear stress has mostly been investigated qualitatively. The quantitative measurement of shear stress, as well as the potential control of the force exerted by an oscillating or a collapsing bubble near rigid and elastic surfaces, remain challenging. The CaviStress project consequently focuses on the quantification of bubble-induced shear stress, through theoretical, numerical and experimental investigations of the interplay between a cavitation bubble and an in-vicinity interface. The main objective of the project is the control and optimization of wall-near stresses induced by oscillating or collapsing bubbles, and its application in two different fields: (i) the cleaning of solid surfaces, and (ii) the molecular uptake of biological cells. We investigate theoretically and numerically the shear stress induced by oscillating and collapsing bubbles both in bulk fluid, and near rigid and elastic walls. The bubble-induced liquid flows are derived theoretically. The fundamental findings are compared to controlled experiments, from the single bubble case to a realistic multibubble streamer where turbulence and mixing occur. Once the liquid flows are characterized, the shear stress is theoretically and numerically quantified. Experimental investigation of the impact of shear stress on rigid walls focuses on its scaling dependence, thus allowing to identify parameter ranges where damage-free cleaning of sensible surfaces is feasible. In parallel, experimental studies of the shear stress on elastic walls focus on the penetration of molecules into biological cells by evaluating the cell poration efficiency from well controlled oscillating or collapsing bubbles. The expected quantification and differentiation of the bubble-induced mechanical effects pave the way towards improved ultrasound based procedures for cleaning and drug delivery through bubbles.

In 2021, the Nobel Committee for Physics reminded that, in a context of global warming, the modern understanding of the variability of the Earth’s climate is based on the existence of clear separations of processes in terms of space and time scales, whose prediction requires interdisciplinary efforts. Fluid mechanics can therefore be an important contributor to the understanding of these fundamental questions, by providing answers about the interaction between large and small-scale structures in the atmosphere, and how their coupled interaction produces significant velocity and temperature fluctuations. In addition to this geostrophic turbulence, almost two-dimensional, that dominates large scales, gravity waves dominate smaller scale dynamics at mid-latitudes, and three-dimensional turbulent fields act at small scales and contribute strongly to vertical mixing and dissipation. The current project is devoted to the understanding, prediction and modeling of large-scale/waves/micro-turbulence interaction phenomena which are characteristic of the atmosphere and of its variability. It relies on: (a) theoretical developments of transport equations of statistical moments of order up to 4, thus giving access to energy fluxes and extreme events in velocity-temperature fields; (b) high resolution direct numerical simulations providing detailed data of different interactions, in idealized conditions; (c) the atmospheric model WRF for predictions with realistic conditions but with a parameterization of small scales. One important outcome of the project will be a model for accurate prediction of atmospheric variability phenomena, and the numerical database it will produce.