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Giorgio Krstulovic

Publications and source records attributed to Giorgio Krstulovic.

At least 73 records · Page 4Linked to original sources
arXiv2016

Statistical steady state in turbulent droplet condensation

Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations we show that the turbulent fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. Based on that, we propose a Lagrangian stochastic model for condensation and evaporation of small droplets in turbulent flows. It consists of a set of stochastic integro-differential equations for the joint evolution of the squared radius and the supersaturation along the droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution. These results reconcile those of earlier numerical studies, once these various regimes are considered.

physics.flu-dyn↗
arXiv2016

Grid superfluid turbulence and intermittency at very low temperature

Low-temperature grid generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states. Results are later confronted with the (quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality of the statistics. For this flow, the statistics are found to be intermittent and a Kolmogorov constant close to the one of classical fluid is found for the second order structure function.

cond-mat.other↗
arXiv2016

A Vortex Filament Tracking Method for the Gross-Pitaevskii Model of a Superfluid

We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.

physics.flu-dyn↗
arXiv2016

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then studied showing that linked rings may appear during the decay. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.

physics.flu-dyn↗
arXiv2015

A lattice model for the Eulerian description of heavy particle suspensions

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase-space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier-Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. This demonstrates the suitability of the proposed approach at large Stokes numbers or for situations where details of collision processes are important.

physics.flu-dyn↗
arXiv2014

Turbulent pair dispersion as a continuous-time random walk

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This approach suggests that the logarithm of the distance between tracers self-averages and performs a continuous-time random walk. This leads to specific predictions for the probability distribution of separations, that differ from those obtained using scale-dependent eddy-diffusivity models (e.g. in the framework of Richardson's approach). Such predictions are tested against high-resolution simulations and shed new lights on the explosive separation between tracers.

physics.flu-dyn↗
arXiv2014

Structures and Lagrangian statistics of the Taylor-Green Dynamo

The evolution of a Taylor-Green forced magnetohydrodynamic (MHD) system showing dynamo activity is analyzed via direct numerical simulations. The statistical properties of the velocity and magnetic field in Eulerian coordinates and along trajectories of fluid elements (Lagrangian coordinates) are found to change between the kinematic, non-linear and saturated regime. Fluid element (tracer) trajectories change from chaotic quasi-isotropic (kinematic phase) to mean magnetic field aligned (saturated phase). The probability density functions (PDFs) of the magnetic field change from strongly non-Gaussian in the kinematic to quasi-Gaussian PDFs in the saturated regime so that their flatness give a precise handle on the definition of the limiting points of the three regimes. Also the statistics of the fluctuations of the kinetic and magnetic energy along fluid trajectories change. All this goes along with a dramatic increase of the correlation time of velocity and magnetic field fluctuations experienced by tracers significantly exceeding one turbulent large-eddy turn-over time. A remarkable consequence is an intermittent scaling regime of the Lagrangian magnetic field structure functions at unusually long time scales.

physics.flu-dyn↗
arXiv2014

Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles

Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong front-like discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.

physics.flu-dyn↗
arXiv2013

Effective rates in dilute reaction-advection systems for the annihilation process $A + A \to \varnothing$

A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non- reacting trajectories. In this limit, it is shown that the moments of the number of particles have an exponential decay rather than the algebraic prediction of standard mean-field approaches. The effective reaction rate is then related to Lagrangian pair statistics by a large-deviation principle. A phenomenological model is introduced to study the qualitative behavior of the effective rate as a function of the interaction length, the degree of chaoticity of the dynamics and the compressibility of the carrier flow. Exact computations, obtained via a Feynman-Kac approach, in a smooth, compressible, random delta-correlated-in-time Gaussian velocity field support the proposed heuristic approach.

nlin.CD↗
arXiv2012

Kelvin-wave cascade and dissipation in low-temperature superfluids vortices

We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked. This procedure directly allows us to obtain the Kevin-waves occupation-number spectrum. Numerical data obtained from long time integration and ensemble-average over initial conditions supports the spectrum proposed in [L'vov and Nazarenko, JETP Lett 91, 428 (2010)]. Kelvin wave modes in the inertial range are found to be Gaussian as expected by weak-turbulence predictions. Finally the dissipative range of the Kelvin-wave spectrum is studied. Strong non-Gaussian fluctuations are observed in this range.

cond-mat.other↗
arXiv2012

Mass fluctuations and diffusion in time-dependent random environments

A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large times with a displacement distribution that approaches a Gaussian. The collective dynamics of diffusing particles reaches a statistically stationary state, which is characterized in terms of a fluctuating mass density field. The probability distribution of density is studied numerically for both smooth and non-smooth scale-invariant random environments. A competition between trapping in the regions where the ejection rate of the environment vanishes and mixing due to its temporal dependence leads to large fluctuations of mass. These mechanisms are found to result in the presence of intermediate power-law tails in the probability distribution of the mass density. For spatially differentiable environments, the exponent of the right tail is shown to be universal and equal to -3/2. However, at small values, it is found to depend on the environment. Finally, spatial scaling properties of the mass distribution are investigated. The distribution of the coarse-grained density is shown to posses some rescaling properties that depend on the scale, the amplitude of the ejection rate, and the Hölder exponent of the environment.

nlin.CD↗
arXiv2011

Axial dipolar dynamo action in the Taylor-Green vortex

We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight in some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super/sub critical nature of the dynamo transition is given.

nlin.CD↗
arXiv2011

Anomalous vortex ring velocities induced by thermally-excited Kelvin waves and counterflow effects in superfluids

Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual friction effects are produced and a dilatation of vortex rings is obtained at large counterflow. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally exited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid $^4{\rm He}$.

cond-mat.stat-mech↗
arXiv2011

Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation

The statistical equilibria of the dynamics of the Gross-Pitaevskii Equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand canonical distributions.. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact low-temperature results. A standard second-order $λ$-transition is exhibited. A new mechanism of GPE thermalization through a direct cascade of energy is found using initial conditions with mass and energy distributed at large scales. A long transient with partial thermalization at small-scales is observed. Vortices are shown to disappear as a prelude to final thermalization and their annihilation is related to the contraction of vortex rings due to mutual friction. Increasing the amount of dispersion at truncation wavenumber is shown to slowdown thermalization and vortex annihilation. A bottleneck that produces spontaneous effective self truncation with partial thermalization is characterized in the limit of large dispersive effects. Metastable counter-flow states are generated using the SGLE algorithm. Spontaneous nucleation of vortex ring is observed and the corresponding Arrhenius law is characterized. Dynamical counter-flow effects on vortex evolution are investigated. Longitudinal effects are produced and measured. A dilatation of vortex rings is obtained for larger counterflows. The vortex ring longitudinal velocity has a strong dependence on temperature, an effect that is related to the presence of finite-amplitude Kelvin waves. This anomalous vortex ring velocity is quantitatively reproduced by assuming equipartition of energy of the Kelvin waves. Orders of magnitude are given for the predicted effects in weakly interacting Bose-Einstein condensates and superfluid $^4{\rm He}$.

cond-mat.stat-mech↗
arXiv2011

Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates

A new mechanism of thermalization involving a direct energy cascade is obtained in the truncated Gross-Pitaevskii dynamics. A long transient with partial thermalization at small-scales is observed before the system reaches equilibrium. Vortices are found to disappear as a prelude to final thermalization. A bottleneck that produces spontaneous effective self-truncation and delays thermalization is characterized when large dispersive effects are present at the truncation wavenumber. Order of magnitude estimates indicate that self-truncation takes place in turbulent Bose-Einstein condensates. This effect should also be present in classical hydrodynamics and models of turbulence.

physics.flu-dyn↗
arXiv2011

Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics

We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to $4096^2$, for which several quadratic invariants are preserved by the truncation and the statistical equilibria are known. Initial conditions are the Orszag-Tang vortex with a neutral X-point centered on a stagnation point of the velocity field in the large scales. In MHD, we observe that the total energy spectra at intermediate times and intermediate scales correspond to the interactions of eddies and waves, $E_T(k)\sim k^{-3/2}$. Moreover, no dissipative range is visible neither for Euler nor for MHD in two dimensions; in the former case, this may be linked to the existence of a vanishing turbulent viscosity whereas in MHD, the numerical resolution employed may be insufficient. When imposing a uniform magnetic field to the flow, we observe a lack of saturation of the formation of small scales together with a significant slowing-down of their equilibration, with however a cut-off independent partial thermalization being reached at intermediate scales.

nlin.CD↗
arXiv2009

Comment on "Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascade". [arXiv:0905.0159v1]

In this comment we point out that the high wavenumber $k^{-3}$ power-law observed by the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] is an artifact stemming from the definition of the kinetic energy spectra and is thus not directly related to a Kelvin wave cascade. We also clarify a confusion about the wavenumber intervals on which Kolmogorov and Kelvin wave cascades are expected to take place.

nlin.CD↗