arXiv subjects

Andrea Mazzino

Publications and source records attributed to Andrea Mazzino.

At least 37 records · Page 2Linked to original sources

arXiv2017

Eddy diffusivity of quasi-neutrally-buoyant inertial particles

We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid which is also constant. Our approach differs from the usual over-damped expansion inasmuch we do not assume a separation of time scales between thermalization and small-scale convection effects. For general incompressible flows, we derive closed-form cell equations for the auxiliary quantities determining the terminal velocity and effective diffusivity. In the special case of parallel flows these equations admit explicit analytic solution. We use parallel flows to show that our approach enables to shed light onto the behavior of terminal velocity and effective diffusivity for Stokes numbers of the order of unity.

physics.flu-dyn↗

arXiv2017

Passive control of a falling sphere by elliptic-shaped appendages

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface imperfections or appendages that serve a function -- are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.

physics.flu-dyn↗

arXiv2016

Eddy diffusivities of inertial particles in random Gaussian flows

We investigate the large-scale transport of inertial particles. We derive explicit analytic expressions for the eddy diffusivities for generic Stokes times. These latter expressions are exact for any shear flow while they correspond to the leading contribution either in the deviation from the shear flow geometry or in the Péclet number of general random Gaussian velocity fields. Our explicit expressions allow us to investigate the role of inertia for such a class of flows and to make exact links with the analogous transport problem for tracer particles.

physics.flu-dyn↗

arXiv2016

Combined role of molecular diffusion, mean streaming and helicity in the eddy diffusivity of short-correlated random flows

We analytically investigate the effective-diffusivity tensor of a tracer particle in a fluid flow endowed with a short correlation time. By means of functional calculus and a multiscale expansion, we write down the main contributions to the eddy diffusivity due to each single physical effect and to their interplays. Namely, besides molecular diffusivity and a constant uniform mean streaming, we take into account the possibility for the (incompressible, Gaussian, stationary, homogeneous, isotropic) turbulent fluctuations to break parity invariance. With respect to the classical turbulence-driven diffusivity amplification for delta-correlated flows, we find that the presence of a short temporal correlation induces a diminution even when coupled with such effects, with two principal exceptions. Notably, the diffusivity is --- perturbatively --- enlarged not only by the helical contribution itself, but also by the interference between molecular diffusion and mean flow.

physics.flu-dyn↗

arXiv2011

Eddy diffusivities of inertial particles under gravity

The large-scale/long-time transport of inertial particles of arbitrary mass density under gravity is investigated by means of a formal multiple-scale perturbative expansion in the scale-separation parametre between the carrier flow and the particle concentration field. The resulting large-scale equation for the particle concentration is determined, and is found to be diffusive with a positive-definite eddy diffusivity. The calculation of the latter tensor is reduced to the resolution of an auxiliary differential problem, consisting of a coupled set of two differential equations in a (6+1)-dimensional coordinate system (3 space coordinates plus 3 velocity coordinates plus time). Although expensive, numerical methods can be exploited to obtain the eddy diffusivity, for any desirable non-perturbative limit (e.g. arbitrary Stokes and Froude numbers). The aforementioned large-scale equation is then specialized to deal with two different relevant perturbative limits: i) vanishing of both Stokes time and sedimenting particle velocity; ii) vanishing Stokes time and finite sedimenting particle velocity. Both asymptotics lead to a greatly simplified auxiliary differential problem, now involving only space coordinates and thus easy to be tackled by standard numerical techniques. Explicit, exact expressions for the eddy diffusivities have been calculated, for both asymptotics, for the class of parallel flows, both static and time-dependent. This allows us to investigate analytically the role of gravity and inertia on the diffusion process by varying relevant features of the carrier flow, as e.g. the form of its temporal correlation function. Our results exclude a universal role played by gravity and inertia on the diffusive behaviour: regimes of both enhanced and reduced diffusion may exist, depending on the detailed structure of the carrier flow.

physics.flu-dyn↗

arXiv2009

Scaling regimes of 2d turbulence with power law stirring: theories versus numerical experiments

We inquire the statistical properties of the pair formed by the Navier-Stokes equation for an incompressible velocity field and the advection-diffusion equation for a scalar field transported in the same flow in two dimensions (2d). The system is in a regime of fully developed turbulence stirred by forcing fields with Gaussian statistics, white-noise in time and self-similar in space. In this setting and if the stirring is concentrated at small spatial scales as if due to thermal fluctuations, it is possible to carry out a first-principle ultra-violet renormalization group analysis of the scaling behavior of the model. Kraichnan's phenomenological theory of two dimensional turbulence upholds the existence of an inertial range characterized by inverse energy transfer at scales larger than the stirring one. For our model Kraichnan's theory, however, implies scaling predictions radically discordant from the renormalization group results. We perform accurate numerical experiments to assess the actual statistical properties of 2d-turbulence with power-law stirring. Our results clearly indicate that an adapted version of Kraichnan's theory is consistent with the observed phenomenology. We also provide some theoretical scenarios to account for the discrepancy between renormalization group analysis and the observed phenomenology.

nlin.CD↗

arXiv2009

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.

nlin.SI↗

arXiv2009

On scaling and statistical geometry in passive scalar turbulence

We show that the statistics of a turbulent passive scalar at scales larger than the pumping may exhibit multiscaling due to a weaker mechanism than the presence of statistical conservation laws. We develop a general formalism to give explicit predictions for the large scale scaling exponents in the case of the Kraichnan model and discuss their geometric origin at small and large scale.

nlin.CD↗

arXiv2008

Renormalized transport of inertial particles in surface flows

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, in which the effect of recirculations is modelled by an oscillatory component in the Eulerian time correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare the efficiency of diffusive and ballistic transport.

nlin.CD↗

arXiv2008

Phase-field model for the Rayleigh--Taylor instability of immiscible fluids

The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase field) whose variation is continuous across the interfacial layers and is uniform in the bulk region. The phase field model obeys a Cahn--Hilliard equation and is two-way coupled to the standard Navier--Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity-capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of nonzero viscosity. In the latter situation only upper and lower bounds for the perturbation growth-rate are known. Finally, we have also investigated the weakly-nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in perfect agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable tecnhique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence enter into play.

physics.flu-dyn↗

arXiv2007

3D chaotic model for sub-grid turbulent dispersion in Large Eddy Simulations

We introduce a 3D multiscale kinematic velocity field as a model to simulate Lagrangian turbulent dispersion. The incompressible velocity field is a nonlinear deterministic function, periodic in space and time, that generates chaotic mixing of Lagrangian trajectories. Relative dispersion properties, e.g. the Richardson's law, are correctly reproduced under two basic conditions: 1) the velocity amplitudes of the spatial modes must be related to the corresponding wavelengths through the Kolmogorov scaling; 2) the problem of the lack of "sweeping effect" of the small eddies by the large eddies, common to kinematic simulations, has to be taken into account. We show that, as far as Lagrangian dispersion is concerned, our model can be successfully applied as additional sub-grid contribution for Large Eddy Simulations of the planetary boundary layer flow.

nlin.CD↗

arXiv2007

Point-source scalar turbulence

The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the spectrum, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is in the injection mechanism, the advecting velocity here being statistically homogeneous and isotropic. Our main results can be summarized as follows. 1) For a very large velocity integral scale, a pure scaling behaviour in the distance between the two points emerges only if their separation is much smaller than their distance from the point source. 2) The value we have found for the scaling exponent suggests the existence of a direct cascade, in spite of the fact that here the forcing integral scale is formally set to zero. 3) The combined effect of a finite inertial-range extension and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that we have quantified and discussed.

nlin.CD↗

arXiv2006

Rayleigh--Taylor turbulence in two dimensions

The first consistent phenomenological theory for two and three dimensional Rayleigh--Taylor (RT) turbulence has recently been presented by Chertkov [Phys. Rev. Lett. {\bf 91} 115001 (2003)]. By means of direct numerical simulations we confirm the spatio/temporal prediction of the theory in two dimensions and explore the breakdown of the phenomenological description due to intermittency effects. We show that small-scale statistics of velocity and temperature follow Bolgiano-Obukhov scaling. At the level of global observables we show that the time-dependent Nusselt and Reynolds numbers scale as the square root of the Rayleigh number. These results point to the conclusion that Rayleigh-Taylor turbulence in two and three dimensions, thanks to the absence of boundaries, provides a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive ``ultimate state of thermal convection''.

nlin.CD↗

arXiv2006

Coarse-grained description of a passive scalar

The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from closed equations for two-point statistical indicators. With the aim of performing a fully-analytical study, the Kraichnan advection model is considered. The white-in-time character of the latter model indeed leads to closed equations for the equal-time scalar correlation functions. The classical closure problem however still arises if a standard filtering procedure is applied to those equations in the spirit of the large-eddy-simulation strategy. We show both how to perform exact closures and how to identify the corresponding coarse-grained scalar evolution.

nlin.CD↗

arXiv2005

Does multifractal theory of turbulence have logarithms in the scaling relations?

The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present.

nlin.CD↗

arXiv2004

Active and passive fields face to face

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behavior is akin to that of its co-evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in two-dimensional magnetohydrodynamics the magnetic potential performs an inverse cascade while the passive scalar cascades toward the small-scales; in surface flows, albeit both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These dramatic differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behavior of dissipative anomalies is addressed.

nlin.CD↗

arXiv2003

Onset and universality of drag reduction in the turbulent Kolmogorov flow

We investigate the phenomenon of drag reduction in a viscoelastic fluid model of dilute polymer solutions. By means of direct numerical simulations of the three-dimensional turbulent Kolmogorov flow we show that drag reduction takes place above a critical Reynolds number $Re_c$. An explicit expression for the dependence of $Re_c$ on polymer elasticity and diffusivity is derived. The values of the drag coefficient obtained for different fluid parameters collapse onto a universal curve when plotted as a function of the rescaled Reynolds number $Re/Re_c$. The analysis of the momentum budget allows to gain some insight on the physics of drag reduction, and suggests the existence of a maximum drag reduction asymptote.

nlin.CD↗

arXiv2001

Scaling and universality in turbulent convection

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.

nlin.CD↗