arXiv subjects

Dario Vincenzi

Publications and source records attributed to Dario Vincenzi.

At least 19 recordsLinked to original sources

arXiv2026

Forcing regimes in the two-dimensional Navier-Stokes equations

In the standard theoretical setting of body-forced turbulence, the forcing that sustains the flow is concentrated in a narrow range of length scales. However, in experiments of fractal-grid turbulence and in numerical simulations inspired by the renormalization group approach, more general forcing functions have been considered. These studies have shown that the phenomenology of turbulence is sensitive to the regularity of the forcing, which raises the wider question of the sensitivity of all Navier--Stokes mathematical estimates to the regularity of body forces. To answer this question, it is necessary to convert the traditional estimates based on the Grashof number, a dimensionless measure of the magnitude of the forcing, to a form dependent on the Reynolds number, the usual dimensionless number in experimental measurements and statistical theories of turbulence. To investigate these issues we consider the two-dimensional case and employ the full range of forcing regularity allowed by the theory of weak solutions to extend available estimates not only for the energy and enstrophy dissipation rates, but also for the dimension of the global attractor. What emerges is the existence of three distinct regimes as a function of the regularity of the forcing.

physics.flu-dyn↗

arXiv2026

How hydrodynamic interactions alter polymer stretching in turbulence

Hydrodynamic interactions (HI) between segments of a polymer have long been known to strongly affect polymer stretching in laminar viscometric flows. Yet the role of HI in fluctuating turbulent flows remains unclear. Using Brownian dynamics simulations, we examine the stretching dynamics of bead-spring chains with inter-bead HI, as they are transported in a homogeneous isotropic turbulent flow (within the ultra-dilute, one-way coupling regime). We find that HI-endowed chains exhibit a steeper coil-stretch transition as the elastic relaxation time is increased, i.e., HI cause less stretching of stiff polymers and more stretching of moderately to highly elastic polymers. The probability distribution function of the end-to-end extension is also modified, with HI significantly limiting the range of extensions over which a power-law range appears. On quantifying the repeated stretching and recoiling of chains by computing persistence time distributions, we find that HI delays migration between stretched and coiled states. These effects of HI, which are consistent with chains experiencing an effective conformation-dependent drag, are sensitive to the level of coarse-graining in the bead-spring model. Specifically, an HI-endowed dumbbell, which cannot form a physical coil, is unable to experience the hydrodynamic shielding effect of HI. Our results highlight the importance of incorporating an extension-dependent drag force in dumbbell-based simulations of turbulent polymer solutions. To develop and test such an augmented dumbbell model, we propose the use of a time-correlated Gaussian random flow, in which the turbulent stretching statistics are shown to be well-approximated.

cond-mat.soft↗

arXiv2026

Is it true that no mathematical relation exists between the Navier-Stokes equations and the multifractal model?

Contrary to accepted turbulence folklore, which holds that no mathematical relation exists between the Navier-Stokes equations (NSEs) and the multifractal model (MFM) of Parisi and Frisch, we develop a theory that reconciles the MFM with Leray's weak solutions of Navier-Stokes analysis. From a combination of Euler invariant scaling and the NSEs set in a three-dimensional box of size $L$, we also derive the Paladin-Vulpiani inverse scale $η_{h,pav}$, which is related to the Reynolds number $\mathit{Re}$ by $Lη_{h,pav}^{-1} = \mathit{Re}^{1/(1+h)}$, and which acts as a mediator between the two theories. This is achieved by considering $L^{2m}$-norms of the velocity gradient to find a correspondence between $m$ and the local scaling exponent $h$ in the multifractal model. The parameter $m$ acts as if it were the sliding focus control on a telescope which allows us to zoom in and out on different structures. The range $1 \leqslant m \leqslant \infty$ is equivalent to $-2/3 \leqslant h_{min} \leqslant 1/3$, which lies precisely in the region where Bandak et al. (2022, 2024) have suggested that thermal noise makes the NSEs inadequate and generates spontaneous stochasticity. The implications of this are discussed.

physics.flu-dyn↗

arXiv2026

Nonlocal flow sampling enables vortex trapping of heavy particles

Most analyses of inertial particle motion in vortical flows rely on the point-particle approximation, in which the fluid velocity is assumed to be linear at the scale of the particle, and for heavy particles inertia typically leads to centrifugal expulsion from vortex cores. Here, we show that a spatially extended particle, modeled as a rigid symmetric dumbbell of two identical inertial point particles connected by a massless rod that samples the flow at two points, can converge to a vortex-centered spinning state. We study the dynamics of this inertial dumbbell in a steady two-dimensional Lamb-Oseen vortex and identify three qualitatively distinct long-time behaviors controlled by the Stokes number. In the weak-inertia limit, the motion remains bounded and traces spirographic-like trajectories around the vortex center, while at sufficiently large inertia centrifugal effects dominate and trajectories spiral outward, approaching inertial point-particle behavior. Between these limits, the dumbbell can reach a trapped spinning state in which the center-of-mass converges to the vortex center and spins steadily, with accessibility determined by the initial conditions. Basin-of-attraction maps and ensemble statistics reveal a non-monotonic dependence of the accessibility of the spinning state on inertia, with basins of finite measure occurring only over an intermediate range of Stokes numbers. Linear stability is governed by the logarithmic slope of the vortex angular-velocity profile, and for the Lamb-Oseen vortex the spinning state is stable for all Stokes numbers. These results highlight how nonlocal flow sampling by spatially extended inertial particles can fundamentally alter transport and long-time behavior in vortical flows.

physics.flu-dyn↗

arXiv2025

Stretching and breaking of particles in compressible random flows

A key feature of turbulent suspensions that involve floating particles on the surface or inertial particles in the bulk is the compressibility of the effective particle-phase velocity field. Little, however, is known about the effects of small-scale flow compressibility on the stretching and breaking of particles. Here, we gain insight into the nature of these effects by studying the deformation of tiny particles in model fluctuating flows. We consider a generic particle with extensional dynamics that are governed by a vector model, which accounts for elasticity, internal viscosity, and non-affine deformation. Applying the dynamical systems approach of Balkovsky, Fouxon & Lebedev (2000), we first obtain general results for the stationary statistics of particle extension in compressible chaotic flows. We then specialize to a time-decorrelated Gaussian random flow and derive an exact solution for the Batchelor regime of the compressible Kraichnan model. We also perform numerical simulations for a time-correlated renewing flow. While straining is suppressed on the average in compressible flows, our results show that large deviations of the strain rate strongly stretch particles and give rise to a power-law distribution of extensions. Extreme straining events are particularly important for stiff particles and, in the examples considered here, give rise to a counter-intuitive effect: stiff particles stretch more and break faster in flows of increasing compressibility. Highly-elastic particles, whose deformation is dictated by the mean straining, stretch less and break slower. Though based on specific random flows, our work shows how compressibility can affect the extensional dynamics of particles by altering the fluctuations of the strain rate, including its large deviations.

physics.flu-dyn↗

arXiv2025

Interface-induced turbulence in viscous binary fluid mixtures

We demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state (NESS) with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. We uncover the properties of this NESS via direct numerical simulations (DNSs) of cellular flows in the Cahn-Hilliard-Navier-Stokes (CHNS) equations for binary fluids. We show that, in this NESS, the shell-averaged energy spectrum $E(k)$ is spread over more than one decade in the wavenumber $k$ and it exhibits a power-law region, indicative of turbulence \textit{but without a conventional inertial cascade}. To characterize the statistical properties of this turbulence, we compute, in addition to $E(k)$, the time series $e(t)$ of the kinetic energy and its power spectrum, scale-by-scale energy transfer as a function of $k$, and the energy dissipation resulting from interfacial stresses. Furthermore, we analyze the mixing properties of this low-Reynolds-number turbulence via the mean-square displacement (MSD) of Lagrangian tracer particles, for which we demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows.

physics.flu-dyn↗

arXiv2025

Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study

We study the stretching of an elastic dumbbell in a turbulent flow, with the aim of understanding and quantifying the effect of hydrodynamic interactions (HI) between the beads of the dumbbell. Adopting the Batchelor-Kraichnan model for the flow, we derive a Fokker-Planck equation and solve it analytically to obtain the probability distribution of the dumbbell's extension. Using different formulations of the HI tensor, we find that HI preferentially enhances the stretching of stiff dumbbells, i.e., those with a small Weissenberg number. We also evaluate the averaging approximations commonly used to simplify the description of HI effects; the consistently-averaged approximation shows that HI result in a less-pronounced coil-stretch transition in chaotic flows. Finally, we confirm the relevance of our analytical results by a comparison with Brownian dynamics simulations of dumbbells transported in a direct numerical simulation of homogeneous isotropic turbulence.

physics.flu-dyn↗

arXiv2024

Dynamics of vorticity moments in shell models of turbulence: A comparison with the Navier-Stokes equations

Shell models allow much greater scale separations than those presently achievable with direct numerical simulations of the Navier-Stokes equations. Consequently, they are an invaluable tool for testing new concepts and ideas in the theory of fully developed turbulence. They also successfully display energy cascades and intermittency in homogeneous and isotropic turbulent flows. Moreover, they are also of great interest to mathematical analysts because, while retaining some of the key features of the Euler and the Navier-Stokes equations, they are much more tractable. A comparison of the mathematical properties of shell models and of the three-dimensional Navier-Stokes equations is therefore essential in understanding the correspondence between the two systems. Here we focus on the temporal evolution of the moments, or $L^{2m}$-norms, of the vorticity. Specifically, differential inequalities for the moments of the vorticity in shell models are derived. The contribution of the nonlinear term turns out to be much weaker than its equivalent for the three-dimensional Navier-Stokes equations. Consequently, pointwise-in-time estimates are shown to exist for the vorticity moments for shell models of any order. This result is also recovered via a high-low frequency slaving argument that highlights the scaling relations between vorticity moments of different orders. Finally, it is shown that the estimates for shell models formally correspond to those for the Navier-Stokes equations 'on a point'.

physics.flu-dyn↗

arXiv2024

Turbulent cascade arrests and the formation of intermediate-scale condensates

Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small scales leads to the arrest of the energy cascade and selection of an intermediate scale, between the forcing and the viscous scales. To investigate the generality of this phenomenon, we study a shell model that is carefully constructed to have three-dimensional turbulent dynamics at small wavenumbers and two-dimensional turbulent dynamics at large wavenumbers. The large scale separation that we can achieve in our shell model allows us to examine clearly the interplay between these dynamics, which leads to an arrest of the energy cascade at a transitional wavenumber and an associated accumulation of energy at the same scale. Such pile-up of energy around the transitional wavenumber is reminiscent of the formation of condensates in two-dimensional turbulence, \textit{but, in contrast, it occurs at intermediate wavenumbers instead of the smallest wavenumber

physics.flu-dyn↗

arXiv2024

An upper critical dimension for dynamo action: A $d$-dimensional closure model study

We construct a $d$-dimensional Eddy Damped Quasi-Normal Markovian (EDQNM) Closure Model to study dynamo action in arbitrary dimensions. In particular, we find lower $d_L$ and upper $d_U$ critical dimensions for sustained dynamo action in this incompressible problem. Our model is adaptable for future studies incorporating helicity, compressible effects and a wide range of magnetic Reynolds and Prandtl numbers.

physics.plasm-ph↗

arXiv2023

Preserving large-scale features in simulations of elastic turbulence

Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: The chaotically advected polymer conformation tensor develops extremely large gradients and can loose its positive definiteness, which triggers numerical instabilities. While efforts to tackle these issues have produced a plethora of specialized techniques -- tensor decompositions, artificial diffusion, and shock-capturing advection schemes -- we still lack an unambiguous route to accurate and efficient simulations. In this work, we show that even when a simulation is numerically stable, maintaining positive-definiteness and displaying the expected chaotic fluctuations, it can still suffer from errors significant enough to distort the large-scale dynamics and flow-structures. Focusing on two-dimensional simulations of the Oldroyd-B and FENE-P equations, we first compare two decompositions of the conformation tensor: symmetric square root (SSR) and Cholesky with a logarithmic transformation (Cholesky-log). While both simulations yield chaotic flows, only the Cholesky-log preserves the pattern of the forcing, i.e., its vortical cells remain ordered in a lattice as opposed to the vortices of the SSR simulations which shrink, expand and reorient constantly. To identify the accurate simulation, we appeal to a hitherto overlooked mathematical bound on the determinant of the conformation tensor, which unequivocally rejects the SSR simulation. Importantly, the accuracy of the Cholesky-log simulation is shown to arise from the logarithmic transformation. We then consider local artificial diffusion, a potential low-cost alternative to high-order advection schemes, and find unfortunately that it significantly modifies the dynamics. We end with an example, showing how the spurious large-scale motions identified here contaminate predictions of scalar mixing.

physics.flu-dyn↗

arXiv2023

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↗

arXiv2023

Polymers in turbulence: stretching statistics and the role of extreme strain-rate fluctuations

Polymers in a turbulent flow are stretched out by the fluctuating velocity gradient; the stationary probability distribution function (p.d.f.) of extensions $R$ has a power-law tail with an exponent that increases with the Weissenberg number $Wi$, a nondimensional measure of polymer elasticity. This study addresses the following questions: (i) What is the role of the non-Gaussian statistics of the turbulent velocity gradient on polymer stretching? (ii) How does the p.d.f. of $R$ evolve to its asymptotic stationary form? Our analysis is based on simulations of the dynamics of finitely-extensible bead-spring dumbbells and chains, in the extremely dilute limit, that are transported in a homogeneous and isotropic turbulent flow, as well as in a Gaussian random flow. First, we recall the large deviations theory of polymer stretching, and illustrate its application. Then, we compare polymer stretching in turbulent and Gaussian random flows and show that while extreme-valued strain rates aid in stretching small-$Wi$ stiff polymers, they are unimportant for high-$Wi$ polymers, which instead are stretched by the cumulative action of moderate strain-rates. This result is supported by an analysis of the persistence time of polymers in stretched states. Next, beginning from a distribution of coiled polymers, we find that the p.d.f. of $R$ has the form of an evolving power-law, for low to moderate $Wi$, though this is not the case at high $Wi$. In either case, the p.d.f. relaxes to its stationary form exponentially. The corresponding time scales of equilibration, measured as a function of $Wi$, point to a critical slowing down at the coil-stretch transition. Importantly, these results show no qualitative change when chains in a turbulent flow are replaced by dumbbells in a Gaussian flow, thereby supporting the use of the latter for reduced-order modelling.

physics.flu-dyn↗

arXiv2022

Spirographic motion in a vortex

Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an inertialess rigid dumbbell in a two-dimensional steady vortex. While the system remains analytically tractable, the particle experiences the nonlinearity of the surrounding velocity field. By exploiting the rotational symmetry of the flow, we reduce the problem to that of a two-dimensional dynamical system, whose fixed points and periodic orbits can be used to explain the motion of the dumbbell. For all vortices in which the fluid angular velocity decreases with radial distance, the center of mass of the dumbbell follows a spirographic trajectory around the vortex center. This results from a periodic oscillation in the radial direction combined with revolution around the center. The shape of the trajectory depends strongly on the initial position and orientation of the dumbbell, but the dynamics is qualitatively the same irrespective of the form of the vortex. If the fluid angular velocity is not monotonic, the spirographic motion is altered by the existence of transport barriers, whose shape is now sensitive to the details of the vortex.

physics.flu-dyn↗

arXiv2021

How to extract a spectrum from hydrodynamic equations

Practical results gained from statistical theories of turbulence usually appear in the form of an inertial range energy spectrum $\mathcal{E}(k)\sim k^{-q}$ and a cut-off wave-number $k_{c}$. For example, the values $q=5/3$ and $\ell k_{c}\sim \mathit{Re}^{3/4}$ are intimately associated with Kolmogorov's 1941 theory. To extract such spectral information from the Navier-Stokes equations, Doering and Gibbon (2002) introduced the idea of forming a set of dynamic wave-numbers $κ_n(t)$ from ratios of norms of solutions. The time averages of the $κ_n(t)$ can be interpreted as the 2$n$th-moments of the energy spectrum. They found that $1 < q \leqslant 8/3$, thereby confirming the earlier work of Sulem and Frisch (1975) who showed that when spatial intermittency is included, no inertial range can exist in the limit of vanishing viscosity unless $q \leqslant 8/3$. Since the $κ_n(t)$ are based on Navier-Stokes weak solutions, this approach connects empirical predictions of the energy spectrum with the mathematical analysis of the Navier-Stokes equations. This method is developed to show how it can be applied to many hydrodynamic models such as the two dimensional Navier--Stokes equations (in both the direct- and inverse-cascade regimes), the forced Burgers equation and shell models.

physics.flu-dyn↗

arXiv2020

Effect of internal friction on the coil-stretch transition in turbulent flows

A polymer in a turbulent flow undergoes the coil-stretch transition when the Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and the relaxation time of the polymer, surpasses a critical value. The effect of internal friction on the transition is studied by means of Brownian dynamics simulations of the elastic dumbbell model in a homogeneous and isotropic, incompressible, turbulent flow and analytical calculations for a stochastic velocity gradient. The results are explained by adapting the large deviations theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic dumbbell with internal viscosity. In turbulent flows, a distinctive feature of the probability distribution of polymer extensions is its power-law behaviour for extensions greater than the equilibrium length and smaller than the contour length. It is shown that although internal friction does not modify the critical Weissenberg number for the coil-stretch transition, it makes the slope of the probability distribution steeper, thus rendering the transition sharper. Internal friction therefore provides a possible explanation for the steepness of the distribution of polymer extensions observed in experiments at large Weissenberg numbers.

physics.flu-dyn↗

arXiv2020

How close are shell models to the 3D Navier-Stokes equations?

Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence. Moreover, they enjoy regularity properties which still remain open for the three-dimensional (3D) Navier-Stokes equations (NSEs). The goal of this study is to make a rigorous comparison between shell models and the NSEs. It turns out that only the estimate of the mean energy dissipation rate is the same in both systems. The estimates of the velocity and its higher-order derivatives display a weaker Reynolds number dependence for shell models than for the 3D NSEs. Indeed, the velocity-derivative estimates for shell models are found to be equivalent to those corresponding to a velocity gradient averaged version of the 3D Navier-Stokes equations (VGA-NSEs), while the velocity estimates are even milder. Numerical simulations over a wide range of Reynolds numbers confirm the estimates for shell models.

nlin.CD↗

arXiv2020

Dynamics of a long chain in turbulent flows: Impact of vortices

We show and explain how a long bead-spring chain, immersed in a homogeneous, isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of 3D turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In 3D, on the contrary, the chain is extended even in vortical regions, which suggests that it follows axially-stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly-flexible, inextensible chain also shows preferential sampling in 3D, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in 2D is considerably reduced. In 3D, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis.

physics.flu-dyn↗