arXiv subjects

Stefano Musacchio

Publications and source records attributed to Stefano Musacchio.

At least 19 recordsLinked to original sources

arXiv2026

The real butterfly effect: from the pop culture to mathematics and physics

The "butterfly effect", introduced over half a century ago by Edward Lorenz, has shifted from a cornerstone of dynamical systems to a popular metaphor, yet its true physical manifestation in fully developed turbulence spans a spectrum of phenomena from standard chaotic sensitivity to the recently established concept of Eulerian spontaneous stochasticity. This paper presents an attempt at a systematic synthesis that brings these different but interconnected ideas together within the unifying framework of the Finite Size Lyapunov Exponent (FSLE). The FSLE describes the growth rate of perturbations as a function of their scale, enabling a comprehensive characterization of the multiscale physics of turbulent flows. Using the FSLE and the Sabra shell model, extended to include thermal noise, we bridge the classical, small-scale Lyapunov regime with predictability at large scales and its interpretation in terms of Eulerian spontaneous stochasticity. Moreover, using the FSLE and the Kraichnan model, we also illustrate the closely related phenomenon of Lagrangian spontaneous stochasticity. To complete the spectrum of butterfly effects, we also examine the "literal butterfly" scenario of localized, sub-dissipative perturbations. Ultimately, this synthesis clarifies the physical mechanisms that dictate the fundamental boundaries of forecasting in high-Reynolds-number flows.

nlin.CD↗

arXiv2026

A new form of mixing in turbulent sedimentation

We study the sedimentation of finite-size inertial particles in a Rayleigh-Taylor-like setup using state-of-the-art direct numerical simulations. The falling particles are observed to produce two distinct regions: a leading mixing layer with a linear concentration profile followed by a bulk region of uniform density. Unlike classical RT turbulence, the mixing layer extension accelerates with an anomalous, non-integer exponent, while the bulk region moves at a constant velocity. A one-dimensional model based on a local hindered settling law accurately captures the observed dynamics and its dependence on the particle-to-fluid density ratio. The present work identifies a new regime of convective mixing which develops at the front of particle suspensions in sedimentation processes.

physics.flu-dyn↗

arXiv2025

Lagrangian chaos and the enstrophy cascade in Ekman-Navier-Stokes two-dimensional turbulence

Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction, the enstrophy flux is suppressed in the cascade and, as a consequence, the small-scale vorticity field becomes passively transported by the large-scale, chaotic flow. We numerically address this problem by investigating how the statistics of the Lagrangian Finite Time Lyapunov Exponent in 2D Ekman-Navier-Stokes simulations are affected by the friction coefficient and by the other parameters of the flow. We derive a simple phenomenological model that interpolates the dependence of the Lyapunov exponent on the flow statistics from the large friction limit, where analytical predictions are available, to the small friction region. We find that the distribution of the FTLE around this mean value is always close to a Gaussian, and this allows to make a simple prediction for the correction of the spectral slope of the direct cascade which is in very good agreement with the numerical results.

physics.flu-dyn↗

arXiv2024

Convection in the active layer speeds up permafrost thaw in coarse grained soils

Permafrost thaw is a major concern raised by the ongoing climate change. An understudied phenomenon possibly affecting the pace of permafrost thaw is the onset of convective motions within the active layer caused by the density anomaly of water. Here, we explore the effects of groundwater convection on permafrost thawing using a model that accounts for ice - water phase transitions, coupled with the dynamics of the temperature field transported by the Darcy's flow across a porous matrix. Numerical simulations of this model show that ice thawing in the presence of convection is much faster than in the diffusive case and deepens at a constant velocity proportional to the soil permeability. A scaling argument is able to predict correctly the asymptotic velocity. Since in the convective regime the heat transport is mediated by the coherent motion of thermal plumes across the thawed layer, we find that the depth of the thawing interface becomes highly heterogeneous.

physics.flu-dyn↗

arXiv2024

How small droplets form in turbulent multiphase flows

The formation of small droplets and bubbles in turbulent flows is a crucial process in geophysics and engineering, whose underlying physical mechanism remains a puzzle. In this letter, we address this problem by means of high-resolution numerical simulations, comparing a realistic multiphase configuration with a numerical experiment in which we attenuate the presence of strong velocity gradients either across the whole mixture or in the disperse phase only. Our results show unambiguously that the formation of small droplets is governed by the internal dynamics which occur during the break-up of large drops and that the high vorticity and the extreme dissipation associated to these events are the consequence and not the cause of the breakup.

physics.flu-dyn↗

arXiv2023

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

physics.flu-dyn↗

arXiv2023

Intermittency in turbulent emulsions

We investigate the statistics of turbulence in emulsions of two-immiscible fluids of same density. We compute for the first time velocity increments between points conditioned to be located in the same phase or in different phases and examine their probability density functions (PDF) and the associated structure functions (SF). This enables us to demonstrate that the the presence of the interface reduces the skewness of the PDF at scales below the Kolmogorov-Hinze scale and therefore the magnitude of the energy flux towards the dissipative scales, which is quantified by the third-order SF. The analysis of the higher order SFs shows that multiphase turbulence is more intermittent than single-phase turbulence. In particular, the local scaling exponents of the SFs display a saturation about the Kolmogorov-Hinze scale and below, which indicates the presence of large velocity gradients across the interface. Interestingly, the statistics approach of classic homogeneous isotropic turbulence when significantly increasing the viscosity of the dispersed phase.

physics.flu-dyn↗

arXiv2022

Flocking turbulence of microswimmers in confined domains

We extensively study the Toner-Tu-Swift-Hohenberg model of motile active matter by means of direct numerical simulations in a two-dimensional confined domain. By exploring the space of parameters of the model we investigate the emergence of a new state of active turbulence which occurs when the aligning interactions and the self-propulsion of the swimmers are strong. This regime of flocking turbulence is characterized by a population of few strong vortices, each surrounded by an island of coherent flocking motion. The energy spectrum of flocking turbulence displays a power-law scaling with an exponent which depends weakly on the model parameters. By increasing the confinement we observe that flocking turbulence becomes unstable: after a long transient, characterized by power-law distributed transition times, the system switches to the ordered state of a single giant vortex

physics.flu-dyn↗

arXiv2021

Enhancement of drag and mixing in a dilute solution of rodlike polymers at low Reynolds numbers

We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds number by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent-like chaotic flow with a wide range of active scales. This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field transported by the flow. By comparing the results of numerical simulations of the model in two- and three-dimensions, we show that the phenomena observed are qualitatively independent on the dimensionality of the space.

physics.flu-dyn↗

arXiv2021

Polymer stretching in laminar and random flows: entropic characterization

Polymers in nonuniform flows undergo strong deformation, which in the presence of persistent stretching can result in the coil-stretch transition. This phenomenon has been characterized by using the formalism of nonequilibrium statistical mechanics. In particular, the entropy of the polymer extension reaches a maximum at the transition. We extend the entropic characterization of the coil-stretch transition by studying the differential entropy of the polymer fractional extension in a set of laminar and random velocity fields that are benchmarks for the study of polymer stretching in flow. In the case of random velocity fields, a suitable description of the transition is obtained by considering the entropy of the logarithm of the extension instead of the entropy of the extension itself. Entropy emerges as an effective tool for capturing the coil-stretch transition and comparing its features in different flows.

cond-mat.soft↗

arXiv2021

Instability of a dusty Kolmogorov flow

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.

physics.flu-dyn↗

arXiv2020

Conformal invariance of weakly compressible two-dimensional turbulence

We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse cascade with scaling close to Kolmogorov prediction. In this range of scales, the statistics of zero-vorticity isolines are found to be compatible with those of critical percolation, thus generalizing the results obtained in incompressible Navier-Stokes turbulence.

physics.flu-dyn↗

arXiv2019

Effects of rotation on the bulk turbulent convection

We study rotating homogeneous turbulent convection forced by a mean vertical temperature gradient by means of direct numerical simulations (DNS) in the Boussinesq approximation in a rotating frame. In the absence of rotationour results are in agreement with the "ultimate regime of thermal convection" for the scaling of the Nusselt and Reynolds numbers vs Rayleigh and Prandtl numbers. Rotation is found to increase both $Nu$ and $Re$ at fixed $Ra$ with a maximum enhancement for intermediate values of the Rossby numbers, qualitatively similar, but with stronger intensity, to what observed in Rayleigh-Bénard rotating convection. Our results are interpreted in terms of a quasi-bidimensionalization of the flow with the formation of columnar structures displaying strong correlation between the temperature and the vertical velocity fields.

physics.flu-dyn↗

arXiv2019

Condensate in quasi two-dimensional turbulence

We investigate the process of formation of large-scale structures in a turbulent flow confined in a thin layer. By means of direct numerical simulations of the Navier-Stokes equations, forced at an intermediate scale, we obtain a split of the energy cascade in which one fraction of the input goes to small scales generating the three-dimensional direct cascade. The remaining energy flows to large scales producing the inverse cascade which eventually causes the formation of a quasi two-dimensional condensed state at the largest horizontal scale. Our results shows that the connection between the two actors of the split energy cascade in thin layers is tighter than what was established before: the small scale three-dimensional turbulence acts as an effective viscosity and dissipates the large-scale energy thus providing a viscosity-independent mechanism for arresting the growth of the condensate. This scenario is supported by quantitative predictions of the saturation energy in the condensate.

physics.flu-dyn↗

arXiv2017

Split energy cascade in turbulent thin fluid layers

We discuss the phenomenology of the split energy cascade in a three-dimensional thin fluid layer by mean of high resolution numerical simulations of the Navier-Stokes equations. We observe the presence of both an inverse energy cascade at large scales, as predicted for two-dimensional turbu- lence, and of a direct energy cascade at small scales, as in three-dimensional turbulence. The inverse energy cascade is associated with a direct cascade of enstrophy in the intermediate range of scales. Notably, we find that the inverse cascade of energy in this system is not a pure 2D phenomenon, as the coupling with the 3D velocity field is necessary to guarantee the constancy of fluxes.

physics.flu-dyn↗

arXiv2017

Emergence of chaos in a viscous solution of rods

It is shown that the addition of small amounts of microscopic rods in a viscous fluid at low Reynolds number causes a significant increase of the flow resistance. Numerical simulations of the dynamics of the solution reveal that this phenomenon is associated to a transition from laminar to chaotic flow. Polymer stresses give rise to flow instabilities which, in turn, perturb the alignment of the rods. This coupled dynamics results in the activation of a wide range of scales, which enhances the mixing efficiency of viscous flows.

physics.flu-dyn↗

arXiv2017

Dusty turbulence

The feedback forces exerted by particles suspended in a turbulent flow is shown to lead to a new scaling law for velocity fluctuations associated to a power-spectra $\propto k^{-2}$. The mechanism at play relies on a direct transfer of kinetic energy to small scales through Kelvin--Helmholtz instabilities occurring in regions of high particle density contrast. This finding is confirmed by two-dimensional direct numerical simulations.

physics.flu-dyn↗

arXiv2016

Coherent structures and extreme events in rotating multiphase turbulent flows

By using direct numerical simulations (DNS) at unprecedented resolution we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flow with millions of inertial particles, we quantify -for the first time- the effects of those coherent vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever measurement of the relative importance between Stokes drag, Coriolis force and centripetal forces along the trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.

physics.flu-dyn↗