arXiv subjects

Giorgio Krstulovic

Publications and source records attributed to Giorgio Krstulovic.

At least 55 records · Page 3Linked to original sources

arXiv2020

Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature

The dynamics of an active, finite-size and immiscible impurity in a dilute quantum fluid at finite temperature is characterized by means of numerical simulations of the projected Gross--Pitaevskii equation. The impurity is modeled as a localized repulsive potential and described with classical degrees of freedom. It is shown that impurities of different sizes thermalize with the fluid and undergo a stochastic dynamics compatible with an Ornstein--Uhlenbeck process at sufficiently large time-lags. The velocity correlation function and the displacement of the impurity are measured and an increment of the friction with temperature is observed. Such behavior is phenomenologically explained in a scenario where the impurity exchanges momentum with a dilute gas of thermal excitations, experiencing an Epstein drag.

cond-mat.stat-mech↗

arXiv2020

Kolmogorov and Kelvin wave cascades in a generalized model for quantum turbulence

We performed numerical simulations of decaying quantum turbulence by using a generalized Gross-Pitaevskii equation, that includes a beyond mean field correction and a nonlocal interaction potential. The nonlocal potential is chosen in order to mimic He II by introducing a roton minimum in the excitation spectrum. We observe that at large scales the statistical behavior of the flow is independent of the interaction potential, but at scales smaller than the intervortex distance a Kelvin wave cascade is enhanced in the generalized model. In this range, the incompressible kinetic energy spectrum obeys the weak wave turbulence prediction for Kelvin wave cascade not only for the scaling with wave numbers but also for the energy fluxes and the intervortex distance.

cond-mat.other↗

arXiv2020

A matching theory to characterize sound emission during vortex reconnection in quantum fluids

In a concurrent work, Villois et al. 2020 reported the evidence that vortex reconnections in quantum fluids follow an irreversible dynamics, namely vortices separate faster than they approach; such time-asymmetry is explained by using simple conservation arguments. In this work we develop further these theoretical considerations and provide a detailed study of the vortex reconnection process for all the possible geometrical configurations of the order parameter (superfluid) wave function. By matching the theoretical description of incompressible vortex filaments and the linear theory describing locally vortex reconnections, we determine quantitatively the linear momentum and energy exchanges between the incompressible (vortices) and the compressible (density waves) degrees of freedom of the superfluid. We show theoretically and corroborate numerically, why a unidirectional density pulse must be generated after the reconnection process and why only certain reconnecting angles, related to the rates of approach and separations, are allowed. Finally, some aspects concerning the conservation of centre-line helicity during the reconnection process are discussed.

physics.flu-dyn↗

arXiv2020

Irreversible dynamics of vortex reconnections in quantum fluids

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross--Pitaevskii model. Despite the time-reversibility of the model, we report a clear evidence that the dynamics of the reconnection process is time-irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently in Proment and Krstulovic (arXiv:2005.02047), we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids.

cond-mat.other↗

arXiv2020

Quantum vortex reconnections mediated by trapped particles

Reconnections between quantum vortex filaments in presence of trapped particles are investigated using numerical simulations of the Gross--Pitaevskii equation. Particles are described with classical degrees of freedom and modeled as highly repulsive potentials which deplete the superfluid. First, the case of a vortex dipole with a single particle trapped inside one of the vortices is studied. It is shown that the reconnection takes place at the position of the particle as a consequence of the symmetry breaking induced by it. The separation rate between the reconnecting points is compatible with the known dynamics of quantum vortex reconnections and it is independent of the particle mass and size. After the reconnection, the particle is pushed away with a constant velocity and its trajectory is deflected because of the transverse momentum exchange with the vortex filaments. The momentum exchanges between the particle, the vortex, and a density pulse are characterized. Finally, the reconnection of two linked rings, each of them with several initially randomly distributed particles is studied. It is observed that generically, reconnections take place at the location of trapped particles. It is shown that reconnection dynamics is unaffected for light particles.

physics.flu-dyn↗

arXiv2020

Active and finite-size particles in decaying quantum turbulence at low temperature

The evolution of a turbulent tangle of quantum vortices in presence of finite-size active particles is studied by means of numerical simulations of the Gross-Pitaevskii equation. Particles are modeled as potentials depleting the superfluid and described with classical degrees of freedom following a Newtonian dynamics. It is shown that particles do not modify the building-up and the decay of the superfluid Kolmogorov turbulent regime. It is observed that almost the totality of particles remains trapped inside quantum vortices, although they are occasionally detached and recaptured. The statistics of this process are presented and discussed. The particle Lagrangian dynamics is also studied. At large time scales, the velocity spectrum of particles is reminiscent of a classical Lagrangian turbulent behavior. At time-scales faster than the turnover time associated to the mean inter-vortex distance, the particle motion is dominated by oscillations due to Magnus effect. For light particles a non-classical scaling of the spectrum arises. The particle velocity and acceleration probability distribution functions are then studied. The decorrelation time of the particle acceleration is found to be shorter than in classical fluids, and related to the Magnus force experienced by the trapped particles.

physics.flu-dyn↗

arXiv2020

How trapped particles interact with and sample superfluid vortex excitations

Particles have been used for more than a decade to visualize and study the dynamics of quantum vortices in superfluid helium. In this work we study how the dynamics of a collection of particles set inside a vortex reflects the motion of the vortex. We use a self-consistent model based on the Gross-Pitaevskii equation coupled with classical particle dynamics. We find that each particle oscillates with a natural frequency proportional to the number of vortices attached to it. We then study the dynamics of an array of particles trapped in a quantum vortex and use particle trajectories to measure the frequency spectrum of the vortex excitations. Surprisingly, due to the discreetness of the array, the vortex excitations measured by the particles exhibits bands, gaps and Brillouin zones, analogous to the ones of electrons moving in crystals. We then establish a mathematical analogy where vortex excitations play the role of electrons and particles that of the potential barriers constituting the crystal. We find that the height of the effective potential barriers is proportional to the particle mass and the frequency of the incoming waves. We conclude that large-scale vortex excitations could be in principle directly measured by particles and novel physics could emerge from particle-vortex interaction.

cond-mat.other↗

arXiv2020

A new self-consistent approach of quantum turbulence in superfluid helium

We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is governed by a modified Navier-Stokes equation. The superfluid vortex lines and normal fluid components are fully coupled in a self-consistent manner by the friction force, which induces local disturbances in the normal fluid in the vicinity of vortex lines. The main focus of this work is the numerical scheme for distributing the friction force to the mesh points where the normal fluid is defined and for evaluating the velocity of the normalfluid on the Lagrangian discretization points along the vortex lines. In particular, we show that if this numerical scheme is not careful enough, spurious results may occur. The new scheme which we propose to overcome these difficulties is based on physical principles. Finally, we apply the new method to the problem of the motion of a superfluid vortex ring in a stationary normal fluid and in a turbulent normal fluid.

physics.flu-dyn↗

arXiv2020

Inhomogeneous distribution of particles in co-flow and counterflow quantum turbulence

Particles are today the main tool to study superfluid turbulence and visualize quantum vortices. In this work, we study the dynamics and the spatial distribution of particles in co-flow and counterflow superfluid helium turbulence in the framework of the two-fluid Hall-Vinen-Bekarevich-Khalatnikov (HVBK) model. We perform three-dimensional numerical simulations of the HVBK equations along with the particle dynamics that depends on the motion of both fluid components. We find that, at low temperatures, where the superfluid mass fraction dominates, particles strongly cluster in vortex filaments regardless of their physical properties. At higher temperatures, as viscous drag becomes important and the two components become tightly coupled, the clustering dynamics in the coflowing case approach those found in classical turbulence, while under strong counterflow, the particle distribution is dominated by the quasi-two-dimensionalization of the flow.

cond-mat.other↗

arXiv2019

Phase transition in time-reversible Navier-Stokes equations

We present a comprehensive study of the statistical features of a three-dimensional time-reversible Navier-Stokes (RNS) system, wherein the standard viscosity $ν$ is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the statistical features of the RNS steady states in terms of a non-negative dimensionless control parameter $\mathcal{R}_r$, which quantifies the balance between the fluctuations of kinetic energy at the forcing length scale $\ell_{\rm f}$ and the total energy $E_0$. We find that the system exhibits a transition from a high-enstrophy phase at small $\mathcal{R}_r$, where truncation effects tend to produce partially thermalized states, to a hydrodynamical phase with low enstrophy at large $\mathcal{R}_r$. Using insights from a diffusion model of turbulence (Leith model), we argue that the transition is in fact akin to a continuous phase transition, where $\mathcal{R}_r$ indeed behaves as a thermodynamic control parameter, e.g., a temperature, the enstrophy plays the role of an order parameter, while the symmetry breaking parameter $h$ is (one over) the truncation scale $k_{\rm max}$. We find that the signatures of the phase transition close to the critical point $\mathcal{R}_r^\star$ can essentially be deduced from a heuristic mean-field Landau free energy. This point of view allows us to reinterpret the relevant asymptotics in which the dynamical ensemble equivalence conjectured by Gallavotti, Phys.Lett.A, 223, 1996 could hold true. Our numerics indicate that the low-order statistics of the 3D RNS are indeed qualitatively similar to those observed in direct numerical simulations of the standard Navier-Stokes (NS) equations with viscosity chosen so as to match the average value of the reversible viscosity.

physics.flu-dyn↗

arXiv2019

Clustering and phase transitions in a 2D superfluid with immiscible active impurities

Phase transitions of a finite-size two-dimensional quantum fluid of bosons in presence of impurities are studied by using the truncated Gross-Pitaevskii model. Impurities are described with classical degrees of freedom. A spontaneous clustering of impurities during the thermalization is observed. Depending on the interaction among impurities, such clusters can break due to thermal fluctuations at temperatures where the condensed fraction is still significant. Clustering is found to increase the condensation transition temperature. The condensation and the Berezinskii-Kosterlitz-Thouless transition temperatures are determined numerically and found to strongly depend on the volume occupied by the impurities. A relative increase up to a 20% of their respective values is observed, whereas their ratio remains approximately constant.

cond-mat.stat-mech↗

arXiv2019

Interaction between active particles and quantum vortices leading to Kelvin wave generation

One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantised vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced central-force model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting long-range mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.

physics.flu-dyn↗

arXiv2018

Quantitative estimation of effective viscosity in quantum turbulence

We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations.

cond-mat.quant-gas↗

arXiv2018

Elastic Weak Turbulence: from the vibrating plate to the drum

Weak wave turbulence has been observed on a thin elastic plate in previous work. Here we report theoretical, experimental and numerical studies of wave turbulence in a thin elastic plate submitted to increasing tension. When increasing the tension (or decreasing the bending stiffness of the plate) the plate evolves progressively from a plate into an elastic membrane as in drums. We start from the plate and increase the tension in experiments and numerical simulations. We observe that the system remains in a state of weak turbulence of weakly dispersive waves. This observation is in contrast with what has been observed in water waves when decreasing the water depth, which also changes the waves from dispersive to weakly dispersive. The weak turbulence observed in the deep water case evolves into a solitonic regime. Here no such transition is observed for the stretched plate. We then apply the weak turbulence theory to the membrane case and show with numerical simulations that indeed the weak turbulence framework remains valid for the membrane and no formation of singular structures (shocks) should be expected in contrast with acoustic wave turbulence.

cond-mat.stat-mech↗

arXiv2018

A Kolmogorov spectrum for strongly vibrating plates

In fluid turbulence, energy is transferred from a scale to another by an energy cascade that depends only on the energy dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Remarkably the normal modes of vibrations in elastic plates manifests an energy cascade with the same K41 spectrum in the fully non-linear regime. Moreover, the elastic deformations present large "eddies" together with a myriad of small "crumpling eddies", such that folds, developable cones, and more complex stretching structures, in close analogy with spots, swirls, vortices and other structures in hydrodynamic turbulence. We characterize the energy cascade, the validity of the constant energy dissipation rate over the scales and the role of intermittency via the correlation functions.

nlin.CD↗

arXiv2018

Tumbling dynamics of inertial chains in extensional flow

The dynamics of elongated inertial particles in an extensional flow is studied numerically by performing simulations of freely jointed bead-rod chains. The coil-stretch transition and the tumbling instability are characterized as a function of three parameters: The Peclet number, the Stokes number and the chain length. Numerical results show that in the limit of infinite chain length, particles are trapped in a coiled or stretched state. The coil-stretch transition is also shown to depend non-linearly on the Stokes and Peclet number. Results also reveal that tumbling occurs close to the coil-stretch transition and that the persistence time is a non-linear function of Stokes and Peclet numbers.

physics.flu-dyn↗

arXiv2017

An exact result in strong wave turbulence of thin elastic plates

An exact result concerning the energy transfers between non-linear waves of thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the $\frac{4}{5}$-Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity and the Airy stress function of a plate, is proven to be equal to $-\varepsilon\, \ell$, where $\ell$ is a length scale in the inertial range at which the increments are evaluated and $\varepsilon$ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Letter are valid for both, weak and strong wave-turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

cond-mat.stat-mech↗

arXiv2017

(Non)-universality of vortex reconnections in superfluids

An insight into vortex reconnections in superfluids is presented making use of analytical results and numerical simulations of the Gross--Pitaevskii model. Universal aspects of the reconnection process are investigated by considering different initial vortex configurations and making use of a recently developed tracking algorithm to reconstruct the vortex filaments. We show that during a reconnection event the vortex lines approach and separate always accordingly to the time scaling $ δ\sim t^{1/2} $ with pre-factors that depend on the vortex configuration. We also investigate the behavior of curvature and torsion close to the reconnection point, demonstrating analytically that the curvature can exhibit a self-similar behavior that might be broken by the development of shock-like structures in the torsion.

physics.flu-dyn↗