We investigate three-dimensional turbulence in a stably stratified fluid driven by a vertically sheared Kolmogorov flow using direct numerical simulations of the Boussinesq equations. As stratification increases, mean profiles evolve toward piecewise-linear shapes while layered density structures emerge, with sharp interfaces separating well-mixed bulk layers. These highly stable interfaces form in the low-shear regions of the mean velocity profile and tend to promote flow relaminarisation, while shear-generated turbulence persists in the bulk layers. We analyse turbulent fluctuations, buoyancy transport and its spatial organisation, and flow stability via profiles of the gradient Richardson number Ri_g. The Richardson number in the bulk layers remains of order unity or less, Ri_g ≲ 1, so that efficient turbulent shear production can take place there. Mixing efficiency analysis shows that the Nusselt number scales with the buoyancy Reynolds number Re_b as Nu = 1 + ΓRe_b (with Γ= ε_p / ε), with the data collapsing onto a robust master curve and roughly following a power-law Nu ∼ Re_b^0.8. Further increase of stratification leads to a temporally intermittent turbulent regime, characterised by quasi-periodic bursts. We propose that the transition from stationary turbulence to this temporally intermittent regime is controlled by the buoyancy Reynolds number and highlight the mechanisms disrupting the turbulence and layered structures.

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when r_0, the separation between particles, is below a characteristic length ℓ_t, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when r_0 > ℓ_t. Our study reveals that the scale ℓ_t coincides with the buoyancy length scale L_B over a broad range of configurations until a transitional wave-dominated regime is reached.

Small-scale turbulence and density stratification are two major ingredients shaping the life of marine micro-organisms in the pycnocline. Such tiny particles are rarely spherical, ranging from flat disks to elongated rods. Particle orientation with respect to the flow or to density gradients plays a crucial role in many aspects of phytoplankton's life, e.g. light harvesting for photosynthesis, enhancement of nutrient uptake, optimal navigation and vertical migration. However, it's still unclear how anisotropic particles align in a turbulent pycnocline and how they are able to cope with density stratification. In the present work, we aim to characterize the effects of stratification on the orientation of inertialess non-spherical particles. To achieve this purpose, we performed direct numerical simulations of a mixed Eulerian-Lagrangian model. The flow is described by the Boussinesq equations, which evolve fluid velocity and density fluctuations in a triply periodic cubic domain. The space is initially seeded with spheroidal particles of different shapes (from rods to disks) transported by the flow as passive tracers. Particle orientation evolves in response to velocity gradients according to Jeffery’s dynamics. We have explored different configurations of the parameters' space by changing particle shape, density stratification and turbulence intensity. The statistical properties of orientation are then unveiled by characterizing the particles' distributions and their mean behavior. Moreover, we have inspected the alignment of particles with respect to the flow and to the iso-density surfaces. We have analyzed rotation rates of the particles and compared our results with the case of spherical particles and homogeneous isotropic turbulence. Such outcomes provide a clear picture of the influence of stratification on the orientational dynamics and on its transition from non-stratified to strongly stratified turbulence. Finally, we conclude by discussing the implications of our results for oceanic applications.

Due to the new trend of space economy and to the resulting increase of space objects, Space Surveillance and Space Traffic Management are becoming essential to reduce the risk of in-orbit collisions and of potential on Earth damages from uncontrolled re-entries. Ground based optical observations, where cameras are coupled with telescopes, represent an invaluable resource for space debris monitoring and tracking. Observations from one single site may provide angular celestial coordinates of a space object, but they must be supplemented with filters and astrodynamic models to provide an estimate of the object trajectory. An alternative approach is the use of multi-site optical observations, where images of the same portion of sky collected with different cameras are matched to retrieve the 3D instantaneous position of space objects without the need of a priori knowledge of the object orbit parameters. Therefore, multi-site observations are extremely convenient to track uncontrolled Earth re-entry and close approach, where the orbit parameters are generally not stable. Here we focus on two-cameras systems and we discuss the use of two triangulation methods: one based on analytic geometry, the other one based on projective geometry. As a proof-of-concept, we compare the performance of the two methods in terms of accuracy in the 3D reconstruction on synthetic images that reproduce the night sky – including orbiting objects and stars – from different locations. To simulate realistic data sets, we produced images taking into account the effect of refraction and annual aberration on the stars, and we added gaussian noise to the position of the stars and of the space objects on the images. The comparison between the two methods shows that they are both valuable, with the projective method being more robust against noise.

Suspended particles can significantly alter the fluid properties and, in particular, can modify the transition from laminar to turbulent flow. We investigate the effect of heavy particle suspensions on the linear stability of the Kolmogorov flow by means of a multiple scale expansion of the Eulerian model originally proposed by Saffman (1962). We find that, while at small Stokes numbers particles always destabilize the flow (as already predicted by Saffman in the limit of very thin particles), at sufficiently large Stokes numbers the effect is non-monotonic in the particle mass fraction and particles can both stabilize and destabilize the flow. Numerical analysis is used to validate the analytical predictions. We find that in a region of the parameter space the multiple-scale expansion overestimates the stability of the flow and that this is a consequence of the breakdown of the scale separation assumptions.

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane, and analyse the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and during the well-mixed stage of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes, where inhomogeneity is maximal.

We investigate the effects of turbulent fluctuations on the Lagrangian statistics of absorption of a scalar field by tracer particles, as a model for nutrient uptake by suspended nonmotile microorganisms. By means of extensive direct numerical simulations of an Eulerian-Lagrangian model we quantify, in terms of the Sherwood number, the increase of the scalar uptake induced by turbulence and its dependence on the Peclet and Reynolds numbers. Numerical results are compared with classical predictions for a stationary shear flow extended here to take into account the presence of a restoring scalar flux. We find that mean-field predictions agree with numerical simulations at low Peclet numbers but are unable to describe the large fluctuations of local scalar uptake observed for large Peclet numbers. We also study the role of velocity fluctuations in the local uptake by looking at the temporal correlation between local shear and uptake rate and we find that the latter follows fluid velocity fluctuations with a delay given by Kolmogorov timescale. The relevance of our results for aquatic microorganisms is also discussed.

The monitoring of space debris and satellites orbiting around Earth is an essential topic in the space surveillance. The impact of debris, even of small size, against active spatial installations causes serious damage, malfunctions and potential service interruptions. Collision-avoidance maneuverings are often performed but they require increasingly complex protocols. Density of space debris is now so high that even astronomical observations are often degraded by it. Although it does not affect space weather, it may interfere with weather satellites. We have developed an innovative experimental technique based on stereometry at intercontinental scale to obtain simultaneous images from two optic observatories, installed in Rome (at the Urbe Airport and in Collepardo on the Apennines) and in Malindi (Kenya). From the observations on Earth, it's possible to reconstruct the three-dimensional position and velocity of the objects. The distance between the two observatories is crucial for an accurate reconstruction. In particular, we have considered the sites of Urbe and Collepardo, with a baseline of 80 km, to detected Low-Earth orbits (LEO), while we have considered a baseline of 6000 km, between Urbe and Malindi, to observe geostationary orbits (GEO). We will present the validation of the three-dimensional reconstruction method via a fully synthetic procedure that propagate the satellite trajectory, using SGP4 model and TLEs data (provided by NASA), and generate synthetic photographs of the satellite passage from the two observatories. Then we will compare the synthetic results with the experimental results obtained using real optic systems. The procedure can be automatized to identify unknown space objects and even generalized for an arbitrary number of sites of observation. The identified debris will be added to the catalogue DISCOS (Database and Information System Characterizing Objects in Space) owned by the European Space Agency (ESA) to improve the space surveillance and the ability to intervene in the case of potential risks.

Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag in the absence of boundaries. We show that the amplitude of the mean flow and the turbulence intensity are reduced by increasing particle mass loading with the consequent enhancement of the friction coefficient. Surprisingly, turbulence suppression is stronger for particles of smaller inertia. We understand such a result by mapping the equations for dusty flow, in the limit of vanishing inertia, to a Newtonian flow with an effective forcing reduced by the increase in fluid density due to the presence of particles. We also discuss the negative feedback produced by turbophoresis which mitigates the effects of particles, especially with larger inertia, on the turbulent flow.

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

We investigate numerically the dynamics and statistics of inertial particles transported by stratified turbulence, in the case of particle density intermediate in the average density profile of the fluid. In these conditions, particles tend to form a thin layer around the corresponding fluid isopycnal. The thickness of the resulting layer is determined by a balance between buoyancy (which attracts the particle to the isopycnal) and inertia (which prevents them from following it exactly). By means of extensive numerical simulations, we explore the parameter space of the system and we find that in a range of parameters particles form fractal cluster within the layer.

We study the motion of small inertial particles in stratified turbulence. We derive a simplified model, valid within the Boussinesq approximation, for the dynamics of small particles in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. Conversely, small scale fractal clustering, typical of inertial particles in turbulence, depends on the particle relaxation time and is almost independent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed.

We study the effects of a stable density stratification on the turbulent dynamics of thin fluid layers forced at intermediate scales. By means of a set of high-resolution numerical simulations, performed within the Boussinesq approximation, we investigate how the stratification and confinement affect the mechanisms of kinetic and potential energy transfer. The detailed analysis of the statistics of the energy-dissipation rates and energy-exchange rates and of the spectral fluxes of potential and kinetic energy shows that stratification provides a new channel for the energy transfer towards small scales which reduces the large-scale flux of kinetic energy. We also discuss the role of vortex stretching and enstrophy flux in the transfer of kinetic energy into potential energy at small scales.