Alessio Innocenti

Spanwise-periodic surface patterns are attractive passive devices for damping Tollmien--Schlichting waves and delaying transition, but reported effects are fragmented and at times contradictory. Simulations and biglobal stability analysis show that spanwise sinusoidal waviness on a flat plate, growing with the boundary-layer thickness, raises the critical Reynolds number yet moves transition upstream. The culprit is wall curvature: in the concave valleys it makes the velocity profiles inflectional even at zero streamwise pressure gradient, increasingly so as the waviness grows. The results turn these competing effects into quantitative guidelines for designing wavy surfaces.

The generation of microdroplets via segmentation in microfluidic devices is of interest in many applications, from biochemical to pharmaceutical. This technique permits indeed much higher control on the droplet size, uniformity and generation rate than in standard batch generation processes. In this work we have evaluated the suitability of the open-source software Basilisk to accurately predict microdroplet generation by segmentation. We have validated the numerical tool with analytical solutions for the dynamics of droplets in confined flows, namely with Bretherton theory, and by comparison with literature experimental results. We have then performed several campaigns of numerical simulations for a coaxial device, analyzing the different regimes of droplet generation, and evaluating how the physical and flow parameters affect the production mechanisms and {the diameters of the generated droplets}. Finally we have proposed new scaling laws for the prediction of droplet diameters in the dripping and jetting regimes, refining existing ones by taking into account additional physical effects, like the viscosity ratio.

We report on an investigation of bubble-induced turbulence. Bubbles of a size larger than the dissipative scale cannot be treated as pointwise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, bubble motions may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations with a volume-of-fluid method. In the first part of the work, we perform both two-dimensional and three-dimensional tests in order to determine appropriate numerical and physical parameters. We then carry out a highly resolved simulation of a three-dimensional bubble column, with a set-up and physical parameters similar to those used in laboratory experiments. This is the largest simulation attempted for such a configuration and is only possible thanks to adaptive grid refinement. Results are compared both with experiments and previous coarse-mesh numerical simulations. In particular, the one-point probability density function of the velocity fluctuations is in good agreement with experiments. The spectra of the kinetic energy show a clear scaling. The mechanisms underlying the energy transfer and notably the possible presence of a cascade are unveiled by a local scale-by-scale analysis in physical space. The comparison with previous simulations indicates to what extent simulations not fully resolved may yet give correct results, from a statistical point of view.

Extreme sea waves, although rare, can be notably dangerous when associated with energetic sea states and can generate risks for the navigation. In the last few years, they have been the object of extensive research from the scientific community that helped with understanding the main physical aspects; however, the estimate of extreme waves probability in operational forecasts is still debated. In this study, we analyzed a number of sea-states that occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. For this purpose, we performed phase-resolving simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We produced statistics of the sea-surface elevation field, calculating crest distributions and the probability of extreme events from the analysis of a long time-series of the surface elevation. We found a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, in contrast with a significant underestimate given by the Rayleigh distribution. We then related spectral quantities like angular spreading and wave steepness to the probability of occurrence of extreme events finding an enhanced probability for high mean steepness seas and narrow spectra, in accordance with literature results, finding also that the case study of the reported accident was not amongst the most dangerous. Finally, we related the skewness and kurtosis of the surface elevation to the wave steepness to explain the discrepancy between theoretical and numerical distributions.

Extreme sea waves have a great impact on the safety of navigation and coastal areas, however their prediction in operational forecasts is difficult and is generally based on spectral indices. Numerical simulations of the free surface Euler equations can be of notable help in the understanding of the statistical properties of a given sea state, and therefore to establish also the probability of extreme or rare events. In this study we performed phase-resolved simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We analyzed a number of sea-states occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. Namely, we produced statistics of the wave field, calculating crest distributions and the probability of extreme events from the analysis of long time-series of the surface elevation. The results show a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, while the Rayleigh distribution gives a significant underestimate. We looked for several kind of correlations between spectral quantities like angular spreading and wave steepness and the probability of occurrence of extreme events, finding an enhanced probability for high mean steepness seas and narrow spectra. It is also evident how the case study of the reported accident was not amongst the most dangerous sea states. Relating the skewness and kurtosis of the surface elevation to the wave steepness helped us to understand the discrepancy between theoretical and numerical distributions.

The Lagrangian approach is natural for studying issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model for inhomogeneous turbulent flows, using velocity and acceleration as dynamical variables. The model takes the form of a diffusion process, and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with velocity-based models. We show that this model generalises both the acceleration-based models for homogeneous flows as well as velocity-based generalised Langevin models. The resulting closed model is applied to a channel flow at high Reynolds number, and compared to experiments as well as direct numerical simulations. A hybrid approach coupling the stochastic model with a Reynolds-averaged Navier–Stokes model is used to obtain a self-consistent model, as is commonly used in probability density function methods. Results highlight that most of the acceleration features are well represented, notably the anisotropy between streamwise and wall-normal components and the strong intermittency. These results are valuable, since the model improves on velocity-based models for boundary layers while remaining relatively simple. Our model also sheds some light on the statistical mechanisms at play in the near-wall region.

We apply the weak formalism on the Boussinesq equations to characterize scaling properties of the mean and the standard deviation of the potential, kinetic and viscous energy fluxes in very well-resolved numerical simulations. The local Bolgiano–Oboukhov (BO) length is investigated and it is found that its value may change by an order of magnitude through the domain, in agreement with previous results. We then investigate the scale-by-scale averaged terms of the weak equations, which are a generalization of the Kármán–Howarth–Monin and Yaglom equations. We have not found the classical BO picture, but evidence of a mixture of BO and Kolmogorov scalings. In particular, all the energy fluxes are compatible with a BO local Hölder exponent for the temperature and a Kolmogorov 41 for the velocity. This behaviour may be related to anisotropy and to the strong heterogeneity of the convective flow, reflected in the wide distribution of BO local scales. The scale-by-scale analysis allows us also to compare the theoretical BO length computed from its definition with that empirically extracted through scalings obtained from weak analysis. Scalings are observed, but over a limited range. The key result of the work is to show that the analysis of local weak formulation of the problem is powerful to characterize the fluctuation properties.