We present a new 3D Lagrangian particle model that is able to correctly reproduce tracer diffusion, pair and tetrad dispersion properties in a 3D turbulent flow, statistically homogeneous and isotropic. The velocity field attached to each marked particle is a superposition of wave-numbers logarithmically spaced, and with an energy content in agreement with Kolmogorov spectrum of turbulent kinetic energy. Each velocity component is generated by an Ornstein-Uhlenbeck process with proper inertial range correlation time. Different single particle multi-scale velocity fields are matched together to correctly reproduce spatial correlation of groups of particles, when these are close by. We show that Richardson law for pair dispersion and its extension to the separation of tetrads of particles are correctly reproduced. The Lagrangian particle model is a perfect candidate for sub-grid scale modeling of tracer trajectories in larger scale models: as an application, we present results of Lagrangian turbulence in a convective planetary boundary layer described by means of a Large-eddy simulation.

We present results obtained from high-resolution direct numerical simulations (DNS) of incompressible, statistically homogeneous and isotropic turbulence, up to a Taylor scale based Reynolds number Re-lambda similar or equal to 200 and with millions of heavy particles with different inertia. In our set-up, particles are assumed to be spherical and rigid, they simply move by viscous forces, such as the Stokes drag. The velocity statistics is found to be extremely intermittent, with an almost bi-fractal behavior. Here, we consider also a new data analysis for the stationary distribution of resealed longitudinal velocity difference and further assess the intermittent character of the heavy particles velocities, characterized by the presence of quasi-algebraic tails.

We study the small-scale statistics of active and passive scalar fields, obtained from 3D large- eddy simulations of the atmospheric boundary layer turbulence. The velocity field is anisotropic and inhomogeneous, due to the action of both buoyancy and shear. We focus on scalar fields rare fluctuations dominated by the so-called fronts. Temperature, coupled to the velocity field by the Boussinesq equations, exhibits anomalous scaling and saturation of the scaling exponents to a constant value, due to the presence of thermal fronts. Altough qualitatively similar, the small- scale statistics of a passive tracer advected by the convective flow shows quantitative differences: the large fluctuations of the tracer concentration field distribute differently and appear to be less intermittent than the temperature ones. To better understand these results, the role of boundaries in this problem is discussed.

A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic, incompressible turbulent flows. The model embeds the multi-scale nature of turbulent temporal and spatial correlations, that are essential to reproduce multi-particle dispersion. It is capable to describe the Lagrangian diffusion and dispersion of temporally and spatially correlated clouds of particles. Although the model neglects intermittent corrections, we show that pair and tetrad dispersion results nicely compare with Direct Numerical Simulations of statistically isotropic and homogeneous 3D turbulence. This is in agreement with recent observations that deviations from self-similar pair dispersion statistics are rare events. (C) 2014 AIP Publishing LLC.

Breakup of small tracer-like aggregates is studied by means f numerical simulations in four different flows, namely homogeneous isotropic turbulence, smooth stochastic flow, turbulent channel flow, and developing boundary layer flow.

By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence underrotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scaleleads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. Byseeding the flowwithmillions ofinertialparticles,wequantify--forthefirsttime--theeffects ofthose coherentvertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitativelyshow that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from theentangled interaction of the vertical structures with the turbulent background. Finally, we present the first-evermeasurement of the relative importance between Stokes drag, Coriolis force, and centripetal force along thetrajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusionproperties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.

We present a detailed investigation of particles relative separation in homogeneous isotropic turbulence. We use data from a 3D direct numerical simulations with 10243 collocation points and R? = 300 following the evolution of a large number of passive tracers and heavy inertial particles, with Stokes numbers in the range St ? [0.5,5]. Many studies [1, 2, 3] have focused on the subject, including extensions to the case of particles with inertia [4]. In particular, our simulation aims to investigate extreme events characterizing the distribution of relative dispersion in turbulent flows [5, 6]. To do that, we seed the flow with hundred millions of particles emitted from localized sources in time and in space. Thanks to such huge statistics, we are able to assess in a quantitative way deviations from Richardson's prediction for tracers. Furthermore, we present the same kind of measures for heavy particles to understand how the inertia affects the pair separation statistics. Finally, to disentangle the effects of different turbulent scales, we present measurements based on exit time statistics for both tracer and inertial particles.

The effect of vertical shear on the horizontal dispersion properties of passive tracer particles on the continental shelf of the South Mediterranean is investigated by means of observation and model data. In situ current measurements reveal that vertical gradients of horizontal velocities in the upper mixing layer decorrelate quite fast (similar to 1 day), whereas an eddy-permitting ocean model, such as the Mediterranean Forecasting System, tends to overestimate such decorrelation time because of finite resolution effects. Horizontal dispersion, simulated by the Mediterranean sea Forecasting System, is mostly affected by: (1) unresolved scale motions, and mesoscale motions that are largely smoothed out at scales close to the grid spacing; (2) poorly resolved time variability in the profiles of the horizontal velocities in the upper layer. For the case study we have analysed, we show that a suitable use of deterministic kinematic parametrizations is helpful to implement realistic statistical features of tracer dispersion in two and three dimensions. The approach here suggested provides a functional tool to control the horizontal spreading of small organisms or substance concentrations, and is thus relevant for marine biology, pollutant dispersion as well as oil spill applications.

Results from high resolution numerical simulations of tracer particles emitted from localised sources in homogeneous and isotropic flows are presented. A huge number of tracers are emitted in order to reach an unprecedented statistics concerning particles pairs motion. We show that the far tails of the particles pair separation Probability Distribution Function can not be described by a Richardsonlike distribution, even if finite Reynolds effects are introduced. We argue that to describe extreme event statistics, velocity temporal correlations and non-Gaussian fluctuations must be taken into account.

I will review some recent advancements about the small-scale statistical prop- erties of dilute suspensions of inertial particles, dispersed in turbulent flows. These are very small, but finite size impurities, with a density contrast with respect to the carrier fluid. Examples of heavy inertial particles - with den- sity much larger than the fluid-, are liquid water droplets in air clouds, or dust and chemicals dispersed in the atmosphere.Inertial particles do not simply follow fluid streamlines, and in the simplest approximation they respond to flow fluctuations via a Stokes viscous drag. I will discuss the relative dispersion of pairs of particles, and contrast the Richardson diffusion behaviour observed for Lagrangian tracers, to the in- ertia related regimes observed for heavy particles. These regimes appear because of the uncorrelation between relative velocities for larger and larger inertia. Locally uncorrelated velocities have an impact also on the estimation of the collision rate of same-size particles, that I will compare to the classical Saffman-Turner formula.The results presented are obtained from Direct Numerical Simulations of in- compressible, homogeneous and isotropic 3D turbulent flow, characterised by a Taylor-scale based Reynolds number between Re? ? 200 and Re? ? 400, seeded with inertial particles.

Results from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number Re?~300 are presented. We study point-like passive tracers and heavy particles, at Stokes number St=0.6,1 and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of 1011. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson's self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of - or rarer than - one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.

The statistics of velocity differences between pairs of heavy inertial point particles suspended in an incompressible turbulent flow is studied and found to be extremely intermittent. The problem is particularly relevant to the estimation of the efficiency of collisions among heavy particles in turbulence. We found that when particles are separated by distances within the dissipative subrange, the competition between regions with quiet regular velocity distributions and regions where very close particles have very different velocities (caustics) leads to a quasi bi-fractal behaviour of the particle velocity structure functions. Contrastingly, we show that for particles separated by inertial-range distances, the velocity-difference statistics can be characterized in terms of a local roughness exponent, which is a function of the scale-dependent particle Stokes number only. Results are obtained from high-resolution direct numerical simulations up to 2048 3 collocation points and with millions of particles for each Stokes number.

By characterising the hydrodynamic stresses generated by statistically homogeneous and isotropic turbulence in rigid aggregates, we estimate theoretically the rate of turbulent breakup of colloidal aggregates and the size distribution of the formed fragments. The adopted method combines direct numerical simulation of the turbulent field with a discrete element method based on Stokesian dynamics. In this way, not only is the mechanics of the aggregate modelled in detail, but the internal stresses are evaluated while the aggregate is moving in the turbulent flow. We examine doublets and cluster-cluster isostatic aggregates, where the failure of a single contact leads to the rupture of the aggregate and breakup occurs when the tensile force at a contact exceeds the cohesive strength of the bond. Owing to the different role of the internal stresses, the functional relationship between breakup frequency and turbulence dissipation rate is very different in the two cases. In the limit of very small and very large values, the frequency of breakup scales exponentially with the turbulence dissipation rate for doublets, while it follows a power law for cluster-cluster aggregates. For the case of large isostatic aggregates, it is confirmed that the proper scaling length for maximum stress and breakup is the radius of gyration. The cumulative fragment distribution function is nearly independent of the mean turbulence dissipation rate and can be approximated by the sum of a small erosive component and a term that is quadratic with respect to fragment size.

We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes,obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree ofmode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by atendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales andfrequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are stillconnected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.

Breakup of small aggregates in fully developed turbulence is studied by means ofdirect numerical simulations in a series of typical bounded and unbounded flowconfigurations, such as a turbulent channel flow, a developing boundary layer andhomogeneous isotropic turbulence. The simplest criterion for breakup is adopted,whereby aggregate breakup occurs when the local hydrodynamic stress  "1=2, with" being the energy dissipation at the position of the aggregate, overcomes a giventhreshold cr, which is characteristic for a given type of aggregate. Results show thatthe breakup rate decreases with increasing threshold. For small thresholds, it developsa scaling behaviour among the different flows. For high thresholds, the breakup ratesshow strong differences between the different flow configurations, highlighting theimportance of non-universal mean-flow properties. To further assess the effects offlow inhomogeneity and turbulent fluctuations, the results are compared with thoseobtained in a smooth stochastic flow. Furthermore, we discuss the limitations andapplicability of a set of independent proxies.

Breakup of suspended aggregates is a ubiquitous phenomenon in particle systems andplays an important role in many industrial and environmental processes. Breakup of suspended aggregates is driven by two mechanisms: (1) In impact breakup, aggregate breakup is caused by energetic collisions with solid objects such as walls, moving equipment (e.g. impeller blades) or other particles. Impact breakup is the dominant mechanism for large and strong agglomerates such as found in powder processing or industrial crystallization. (2) In hydrodynamic breakup, aggregate breakup is caused by viscous stress acting on the aggregate. Hydrodynamic breakup is the dominant mechanism for small and weak aggregates where the constituting particles are hold together by Van der Waals or electrostatic forces [1,2].In this work the breakup of small inertial aggregates due to hydrodynamic stress in homogeneous isotropic turbulence is investigated by means of numerical simulations. Hydrodynamic breakup in turbulence is a challenging problem as the viscous stress acting on the aggregate is subject of strong fluctuations, and situations where the hydrodynamic stress overcomes the cohesive strength of the aggregate occur only intermittently and with timescales controlled by turbulent fluid and particle motions. The aim of our study is to determine the frequency at which the hydrodynamic stress acting on an aggregate suspended in a turbulent flow overcomes a predefined threshold value representing the aggregate strength.The resulting frequency is referred to as aggregate breakup rate [3,4] which in this work is determined as a function of the aggregate strength and aggregate inertia.For fixed aggregate inertia, characterized through an aggregate Stokes number, the breakup rate is decreasing with increasing aggregate strength. This implies that vigorous turbulent events that are violent enough to breakup an aggregate become rarer the stronger the aggregate. For small aggregate strength, the decrease of the breakup rate shows power law behavior while for large aggregate strength a sharp drop-off of the breakup rate is observed. With increasing aggregate breakup the contribution of drag acting on the aggregate is increasing. This leads to an increase of the breakup rate. To the authors knowledge this is the first systematic study on the role of drag stress on the breakup of aggregates in turbulence.

In turbulence, ideas of energy cascade and energy flux, substantiated by the exactKolmogorov relation, lead to the determination of scaling laws for the velocity spatialcorrelation function. Here we ask whether similar ideas can be applied to temporalcorrelations. We critically review the relevant theoretical and experimental resultsconcerning the velocity statistics of a single fluid particle in the inertial range of sta-tistically homogeneous, stationary and isotropic turbulence. We stress that the widelyused relations for the second structure function, D2(t) ? ?[v(t) - v(0)]2? ? ?t, re-lies on dimensional arguments only: no relation of D2(t) to the energy cascade isknown, neither in two- nor in three-dimensional turbulence. State of the art experimental and numerical results demonstrate that at high Reynolds numbers, the derivative d D2(t )/dt has a finite non-zero slope starting from T? The analysis of the acceleration spectrum \Phi_A(?) indicates a possible small correction with respect to the dimensional expectation \Phi_A(?) ~ ?_0 but present data are unable to discriminate between anomalous scaling and finite Reynolds effects in the second order moment of velocity Lagrangian statistics.

Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension D. By tuning the fractal dimension parameter, we study the dynamical effects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In particular, we show that as we move from D = 3 to D similar to 2.8, the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretching properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous fluctuations.

Tracer dispersion within a highly convective planetary boundary layer is studied by means of a large-eddy simulation (LES) model for the continuous phases describing the temperature and velocity fields, and with the Lagrangian tracking of particle trajectories. Particle velocities are decomposed into their resolved and unresolved (or sub-grid) components. The former are evaluated by interpolation from the LES velocity field, the latter are given by a Lagrangian kinematic model that correctly describes the turbulent dispersion of clouds of particles. It is shown that, thanks to the Lagrangian sub-grid model, a clear inertial range is detectable in the time domain. In this range, particle separation grows according to Richardson's law, and nicely compares with previous experimental and numerical measurements. The collective motion of four particles, initially located at the vertices of regular tetrahedra, is also studied. The evolution of tetrad shape and orientation is contrasted with those obtained in homogeneous and isotropic flows. Results show that an agreement is achieved at small time lags. At larger times, the boundary layer reveals its anisotropic structure and the tetrad shape statistics deviate from results obtained in ideal flows. © 2014 AIP Publishing LLC.

A large-eddy simulation model is adopted to investigate the evolution of scalars transported by atmospheric cloud-free convective boundary layer flows. Temperature fluctuations due to the ground release of sensible heat and concentration fluctuations of a trace gas emitted at the homogeneous surface are mixed by turbulence within the unstable boundary layer. On the top, the entrainment zone is varied to obtain two distinct situations: (i) the temperature inversion is strong and the trace gas increment across the entrainment region is small, yielding to a small top flux with respect to the surface emission; (ii) the temperature inversion at the top of the convective boundary layer is weak, and the scalar increment large enough to achieve a concentration flux toward the free atmosphere that overwhelms the surface flux. In both cases, an estimation of the entrainment flux is obtained within a simple model, and it is tested against numerical data. The evolution of the scalar profiles is discussed in terms of the different entrainment-surface flux ratios.Results show that, when entrainment at the top of the boundary layer is weak, temperature and trace gas scalar fields are strongly correlated, particularly in the lower part of the boundary layer. This means that they exhibit similar behavior from the largest down to the smallest spatial scales. However, when entrainment is strong, as moving from the surface, differences in the transport of the two scalars arise.Finally, it is shown that, independently of the scalar regime, the temperature field exhibits more intermittent fluctuations than the trace gas.

Droplets, aerosol and other impurities in turbulent flows are typical examples of finite-size particles with a mass density much larger than the carrier fluid, that can not be modeled as point tracers. The knowledge of the statistics of velocity differences between pairs of heavy inertial particles sus- pended in an incompressible turbulent flow is relevant both in the dissipative and in the inertial range of scales. As for the former, it rules the efficiency of collisions between heavy particles in turbulence. While in the latter case, it is important for the statistics of relative dispersion of pairs of particles. We present results obtained from high-resolution direct numerical simulations of incompressible, homogeneous and isotropic turbulence, up to a Taylor scale based Reynolds number Re? ? 400 (with 20483 grid points) and with millions of heavy particles with different inertia [1]. In our set-up, particles assumed to be spherical and rigid, simply move by viscous forces, such as the Stokes drag. The velocity statistics is found to be extremely intermittent. At very small scales, when particles are separated by distances within the dissipative subrange, we found that the competition between regions with quiet regular velocity distributions and regions where very close particles have very different velocities leads to a quasi bi-fractal behaviour of the particle velocity structure functions (moments of particles velocity differences). This points to the existence of quasi-singularities in the statistics of heavy particles velocity. In the limit of small inertia, the particle dynamics approaches that of tracers and consequently the velocity difference over a scale R is essentially coincident with the fluid longitudinal increment over a separation r = R. Conversely, when the inertia becomes very large, particles move ballistically in the flow with uncorrelated velocities and the momnets of velocity differences become independent of the scale R. For intermediate values of the Stokes number, one observes a non-trivial behavior as a function of the scale and of the Stokes number St = ?/??. Here, ? is the particle response time to the fluid, and ?? is the Kolmogorov time scale of the flow.For particles separated by inertial-range distances, we show that the velocity-difference statistics can be characterized in terms of a local roughness exponent, which is a function of the scale-dependent particle Stokes number only, defined as St(r) = ??1/3/r2/3 in terms of the local eddy turnover time.

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re-lambda similar to 200 and Re-lambda similar to 400, corresponding to resolutions of 512(3) and 2048(3) grid points, respectively. Particles Stokes number values range from St approximate to 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv:1012.1789v1 [physics.fludyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

The description of the statistical properties of small inertial particles sus- pended in turbulent flows is an important problem within fluid dynamics in general, and cloud physics in particular. For passively advected particles, in recent years a large number of experi- mental and numerical observations has been collected, mostly in the simplest situation of homogeneous and isotropic turbulence (HIT).I will review some results obtained in direct numerical simulations of HIT about small scale properties of inertial particles velocity statistics and spatial distribution. In particular, I will try to highlight effects for which gravita- tional accelerations matters.

For a solution droplet in equilibrium with the atmospheric environment, a relationship exists between radius and concentration, which allows to express the saturation ratio of the droplet as a function of either one of these two parameters. The curves showing the complete behaviour of saturation ratio as a function of radius, for various sizes of NaCl nuclei, were previously presented for both wholly and partially dissolved salt. Here, the dependence of saturation ratio on droplet concentration, rather than on its radius, is examined and plotted for various NaCl nuclei. The occurrence of an analogous, but X-shaped, hysteresis phenomenon, characterizing the behaviour of the solution concentration in a growing-shrinking cycle of a solution droplet under changing humidity, is evidenced and discussed. An insoluble spherical core is assumed to be always present inside the condensation nucleus, so that the onset of the sudden salt re-crystallization is triggered at a well defined concentration value. © EDP Sciences, 2014.

Coalescence growth of droplets is a fundamental process for liquid cloud evolution. The initiation of collisions and coalescence occurs when a few droplets become large enough to fall. Gravitational collisions represent the most efficient mechanism for multi-disperse solutions, when droplets span a large variety of sizes. However, turbulence provides another mechanism for droplets coalescence, taking place also in the case of uniform condensational growth leading to narrow droplet-size spectra. We consider the problem of estimating the rate of collisions of small droplets dispersed in a highly turbulent medium. The problem is investigated by means of high-resolution direct numerical simulations of a three-dimensional turbulent flow, seeded with inertial particles, up to resolutions of 2048^3 grid points. Rate of collision is estimated in terms of the probability to find particles at close positions, and of the statistics of particles velocity. In particular, we show that the statistics of velocity differences between inertial particles suspended in an incompressible turbulent flow is extremely intermittent. When particles are separated by distances of the order of their diameter, the competition between quiet regular regions and multivalued caustics leads to a quasi bi-fractal behavior of the particle velocity statistics, with high-order moments bringing the signature of caustics. This results in large probabilities that close particles have important velocity differences. Together with preferential concentration of particles in low-vorticity regions, caustics contribute to speed-up collisions between inertial particles. Implications for the early stage of rain droplets formation are discussed.

Knowledge of the link between ocean hydrodynamics and distribution of small pelagic fish species is fundamental for the sustainable management of fishery resources. Both commercial and scientific communities are indeed seeking to provide services that could "connect the dots" among in situ and remote observations, numerical ocean modelling, and fisheries. In the Mediterranean Sea and, in particular, in the Sicily Channel the reproductive strategy of the European Anchovy (Engraulis encrasicolus) is strongly influenced by the oceanographic patterns, which are often visible in sea surface temperature satellite data. Based on these experimental evidences, we propose here a more general approach where the role of ocean currents, wind effects, and mesoscale activity are tied together. To investigate how these features affect anchovy larvae distribution, we pair ichthyoplankton observations to a wide remote sensing data set, and to Lagrangian numerical simulations for larval transport. Our analysis shows that while the wind-induced coastal current is able to transport anchovy larvae from spawning areas to the recruiting area off the Sicilian south-eastern tip, significant cross-shore transport due to the combination of strong northwesterly mistral winds and topographic effects delivers larvae away from the coastal conveyor belt. We then use a potential vorticity approach to describe the occurrence of larvae cross-shore transport. We conclude that monitoring and quantifying the upwelling on the southern Sicilian coast during the spawning season allows to estimate the cross-shore transport of larvae and the consequent decrease of individuals within the recruiting area.

The diurnal evolution of a cloud free, marine boundary layer is studied by means of experimental measurements and numerical simulations. Experimental data belong to an investigation of the mixing height over inner Danish waters. The mixed-layer height measured over the sea is generally nearly constant, and does not exhibit the diurnal cycle characteristic of boundary layers over land. A case study, during summer, showing an anomalous development of the mixed layer under unstable and nearly neutral atmospheric conditions, is selected in the campaign. Subsidence is identified as the main physical mechanism causing the sudden decrease in the mixing layer height. This is quantified by comparing radiosounding profiles with data from numerical simulations of a mesoscale model, and a large-eddy simulation model. Subsidence not only affects the mixing layer height, but also the turbulent fluctuations within it. By analyzing wind and scalar spectra, the role of subsidence is further investigated and a more complete interpretation of the experimental results emerges. © 2014 Author(s).

A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D = 2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k) similar to k^(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D similar to 2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism.

We present a systematic investigation of 3D turbulent flows evolved on a highly decimated set of Fourier modes. In particular, we investigate the change in small-scales intermittency when the flow is constrained to excite only a fractal set of modes but keeping the symmetries of the original 3D Navier-Stokes equations.

The relative dispersion of pairs of inertial point particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number $Re_{\lambda} \sim 200$ and $Re_{\lambda} \sim 400$, corresponding to resolutions of $512^3$ and $2048^3$ grid points, respectively. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle density ratio. For particles much heavier than the fluid, the range of available Stokes numbers is $St \in [0.1\!:\!70]$, while for light particles the Stokes numbers span the range $St \in [0.1\!:\!3]$ and the density ratio is varied up to the limit of vanishing particle density.\\ For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed, and which is supported by the numerical results.\\ In the case of light particles with high density ratio, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations.