Random Vortex Research Articles

Quantum turbulence of bellows-drivenHe4superflow: Decay

We report on studies of quantum turbulence with second sound in superfluid $^{4}\mathrm{He}$ in which the turbulence is generated by the flow of the superfluid component through a wide square channel, the ends of which are plugged with sintered silver superleaks, the flow being generated by compression of a bellows. The superleaks ensure that there is no net flow of the normal fluid. In an earlier paper [S. Babuin et al., Phys. Rev. B 86, 134515 (2012)] we have shown that steady flow of this kind generates a density of vortex lines that is essentially identical to that generated by thermal counterflow, when the average relative velocity between the two fluids is the same. In this paper we report on studies of the temporal decay of the vortex-line density, observed when the bellows is stopped, and we compare the results with those obtained from the temporal decay of thermal counterflow remeasured in the same channel and under the same conditions. In both cases there is an initial fast decay which, for low enough initial line density, approaches for a short time the form ${t}^{\ensuremath{-}1}$ characteristic of the decay of a random vortex tangle. This is followed at late times by a slower ${t}^{\ensuremath{-}3/2}$ decay, characteristic of the decay of large ``quasiclassical'' eddies. However, in the range of investigated parameters, we observe always in the case of thermal counterflow, and only in a few cases of high steady-state velocity in superflow, an intermediate regime in which the decay either does not proceed monotonically with time or passes through a point of inflexion. This difference, established firmly by our experiments, might represent one essential ingredient for the full theoretical understanding of counterflow turbulence.

Josephson-induced hysteretical behavior of vortex matter in layered BSCCO samples with columnar defects: Bose glass phase and the melting process

We present Monte Carlo simulations of three-dimensional systems of vortex lines in the presence of random columnar defects using the Lawrence-Doniach model with BSCCO parameters. In particular, we study the structure factor and the vortex-vortex correlation length along the field (B) direction, for both intermediate and high fields. Two representative initial conditions at zero temperature (T) are used: the Abrikosov lattice and a random vortex lattice, mimicking possible configurations in a zero-field-cooled (ZFC) protocol, both characterized by smooth plane decoupling transitions (formation of pancake-like vortex structure), with exponential decay with T of the correlation length around the melting transition. The very relevant case of field-cooling (FC) from a melted configuration is also considered. In this case, as T decreases for intermediate B, the system evolves through states of an unpinned vortex lattice phase and metastable states of a phase of unpinned vortices in a Bose glass (BG) background; lastly, the system reaches a FC robust BG phase down to very low T. On the other hand, for high fields and under the ZFC protocol, the melting transition is practically concurrent with the discontinuous decoupling of planes; while, under FC, the vortex lattice decouples much before the melting transition. Indeed, we identify that the exchange between flux lines is the underlying mechanism for plane decoupling and the formation of a pancake-like vortex structure. We stress that the correspondent phase diagram B vs. T is in good agreement with previous experimental results in BSCCO.

Beam wander of random electromagnetic Gaussian-shell model vortex beams propagating through a Kolmogorov turbulence

Beam wander of random electromagnetic Gaussian-Shell model (EGSM) vortex beams propagating through atmospheric turbulence is investigated. We develop the expression for beam wander of random EGSM vortex beams in theory. The effects of topological charge, turbulence strength, initial spatially coherent length, transverse scale, and wavelength on beam wander are illustrated numerically. The numerical results show that vortex beams with both positive and negative topological charges have the same beam wander, decreasing the coherent length and decreasing the transverse scale, or increasing the topological charge, can decrease the beam wander. In free-space optical (FSO) communication, we can choose beams with smaller coherent length, smaller wavelength, and larger topological charge to reduce beam wander.

A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder

A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM) which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.

Influence of topological charges on random wandering of optical vortex propagating through turbulent atmosphere

We investigate the random wandering behavior of optical vortex over propagation distance of 5km in weak turbulence. The multiple random phase screen simulation method and vortex extracting method are utilized to calculate the optical vortex positions (x,y) on the receiver plane. Numerical results reveal that x and y are Gaussian random variables. However, the errors of Gaussian fitting become larger and the Gaussian fitting curves become broader as topological charge of optical vortex increases through the same atmospheric turbulence. Our results are crucial for free-space optical vortex communication.

Large eddy simulations of 2-D and 3-D spatially developing mixing layers

The present work focuses on evaluating and improving the modelling capabilities of the second-order accurate ANSYS-Fluent™ LES implementation for a spatially developing mixing layer. The LES methodology is evaluated by modelling a widely studied problem, a spatially-developing, planar mixing layer and improved by modifying the inflow forcing algorithm available in Fluent to better suit the mixing layer. The latter is one of the main contributions of this work. The suggested inflow modification is applicable to any CFD code, not only Fluent. A low Reynolds number mixing layer is simulated in two- and three-dimensions without the splitter plate walls. The effects of inflow forcing and a buffer zone at the domain exit are investigated using 2-D simulations. The sensitivity of the 2-D results to time-step and grid sizes is also investigated. We present a modified random vortex method (VM) algorithm for inflow forcing in 3-D. The modified VM is based on modelling inflow velocity perturbations through hair-pin vortices of the splitter plate boundary layers to better capture the translative instability and the streamwise vortices of the mixing layer.

Spectral properties of a random electromagnetic partially coherent flat-topped vortex beam in turbulent atmosphere

Based on the extended Huygens–Fresnel principle, we introduced the analytic expression of a random electromagnetic partially coherent flat-topped (PCFT) vortex beam propagating in Kolmogorov atmospheric turbulence. The spectral properties of the random electromagnetic PCFT vortex beam are explored by using the unified theory of coherence and polarization. It is demonstrated by numerical results and found that after propagating through turbulent atmosphere, the spectral density, the spectral degree of polarization as well as the spectral degree of coherence of the random electromagnetic PCFT vortex beam vary. The variations of the spectral properties depend closely on the strength of atmospheric turbulence and the properties of the source beam, i.e. the topological charges, the order of flatness, the waist width as well as the initial spatial coherence. In addition, the distributions of the spectral density and the spectral degree of polarization undergo several stages of evolution and finally tend to Gaussian profile at the receiver plane. Some possible explanations have also been given for these interesting physical phenomena.

On the turbulence generated by the potential surface waves

The turbulence (the random vortex motions) of the upper ocean is nourished by the energy and momentum of the surface waves (the potential motion). The statistical characteristics of the turbulence (turbulent kinetic energy, dissipation rate, and Reynolds stresses) depend on the state of the ocean surface waves. This paper discusses the possibilities of generating this turbulence using the vortex instability of the potential surface waves. The vortex component of fluctuations of velocity field and possibly the interaction between both the vortex and potential motions cause the vertical transport of the momentum. The Reynolds tensor is a linear function of the correlation tensor of vortex field. The initial small vortex perturbations always exist in the upper ocean because of the molecular viscosity influences, especially near the free surface, and the fluctuations of the seawater density. The horizontal inhomogeneities of the seawater density produce the vortex field even if the initial vorticity was zero and the initial flow was the potential flow. The evolution of the small initial vortex disturbances in the velocity field of potential linear surface waves is reduced to a coupled set of linear ordinary differential equations of the first order with periodic coefficients. The solution of this problem shows that the small initial vortex perturbations of potential linear surface waves always grow. The initial small vortex perturbations interacting with the potential surface wave produce the small‐scale turbulence (Novikov's turbulence) that finally causes the viscous dissipation of the potential surface wave. The wave‐induced turbulence can be considered as developed turbulence with a well distinguishable range of the turbulent wave numberskwhere turbulence obeys the Kolmogorov's self‐similarity law.

Crossover between Rayleigh-Taylor instability and turbulent cascading atomization mechanism in the bag-breakup regime

The question of whether liquid atomization depends on instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor, or Kelvin-Helmholtz mechanisms) or on turbulent cascades, as suggested by Richardson and Kolmogorov, is still open. In this paper, experimental results reveal that both mechanisms are needed to explain the probability density functions (PDFs) of the droplets in a spray obtained from an industrial fan spray nozzle. Instability of Rayleigh-Taylor type controls the size of the largest droplets while the smallest droplets follow a PDF given by a turbulent cascading mechanism characterized by a log-Lévy stable law that has a stability parameter equal to 1.70. This value is very close to the inverse value of the Flory exponent and can be related to a recent model developed by N. Rimbert for intermittency modeling stemming from self-avoiding random vortex stretching.

Simulation of a premixed turbulent flame by a conservative level set method

The premixed turbulent V-flame is numerically simulated in this paper. The technique used in Chan et al. [Effect of intense turbulence on turbulent premixed V-flame, Int. J. Eng. Sci. 41 (2003), pp. 903–916; Simulation of a premixed turbulent flame with the discrete vortex method, Int. J. Numer. Methods Eng. 48 (2000), pp. 613–627] was based on the random vortex method and the conventional level set method. However, this paper is an improvement of the previous technique by using a conservative level set method. The new algorithm uses a bi-cubic interpolation process together with Newton's method to reconstruct the velocity field to improve the conservation of the level set method. The numerical example in this paper indicates the efficiency of the new method in solving the problem of turbulent premixed V-flame by comparing the results with available data.

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

The topological susceptibility of the $SU(3)$ random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in $SU(3)$ lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in $SU(3)$ lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.

Finding the Elusive Sliding Phase in the Superfluid-Normal Phase Transition Smeared byc-Axis Disorder

We consider a stack of weakly Josephson coupled superfluid layers with c-axis disorder in the form of random superfluid stiffnesses and vortex fugacities in each layer as well as random interlayer coupling strengths. In the absence of disorder this system has a 3D XY type superfluid-normal phase transition as a function of temperature. We develop a functional renormalization group to treat the effects of disorder, and demonstrate that the disorder results in the smearing of the superfluid-normal phase transition via the formation of a Griffiths phase. Remarkably, in the Griffiths phase, the emergent power-law distribution of the interlayer couplings gives rise to a sliding Griffiths superfluid, with a finite stiffness in the a-b direction along the layers, and a vanishing stiffness perpendicular to it.

Simple model for turbulence intermittencies based on self-avoiding random vortex stretching

Whether statistics of intermittencies (between small and large eddies) in homogeneous and isotropic turbulence should be described by a logarithmic-Poisson, a logarithmic-stable probability density function, or other is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk, and random vortex stretching is established which may help to obtain new insights on this topic. A very simple relationship between the stability index of the Lévy stable law and Flory's exponent stemming from statistics of linear polymer growth is established. Moreover, the scaling of turbulence intermittencies with Reynolds number is also explained and the overall picture is given of smallest vortex tubes of Kolmogorov length width (i.e., the smallest dissipative eddies) bent by bigger vortices of Taylor length scale (i.e., the mean dissipative eddies), themselves stretched by the bigger eddies in a continuous cascade. This results in both a simple and sound model with no fitting parameters required.

Influence of Bilge Keel Width on the Roll Damping of FPSO

Current industry practice to control roll motions in floating production storage and offloading (FPSO) vessels is based on using large-width bilge keels. This paper details an experimental study involving a range of bilge keel widths from 0% to 20% of half beam of a FPSO with rectangular geometry. Both free decay and forced oscillation tests were conducted on the range of geometries at different amplitudes and frequencies. The results show that, for given amplitude of roll motion, the damping coefficient increases with increasing bilge keel size up to a certain point and then declines. Numerical simulations using the free surface random vortex method were performed on rectangular cross sections with bilge keels, which show good agreement with the experimental results. Simulations extended up to even larger keel widths indicate that the same trend for damping coefficient as a function of keel size is found. An examination of the simulation results suggests a likely explanation for this behavior. A simplified formulation for damping coefficient is developed as a function of bilge keel width and roll amplitude.

Simulation study for the orientation of the driven vortex lattice in an amorphous superconductor

We investigate the orientation of the vortex lattice driven by an applied current by means of numerical simulations based on the time-dependent Ginzburg–Landau (TDGL) theory. A lattice order is restored by a current driving of vortices under the influence of random vortex pinnings. The orientation of the moving vortex lattice is different between the presence and the absence of vortex pinnings. We show results of TDGL simulations for these phenomena.

Application of the Random Vortex Method to Natural Convection Heat Transfer from an Open Channel

Natural convection flows in channels have been studied using numerical tools such as finite difference and finite element techniques. These techniques are much demanding in computer skills and memory. Random Vortex Element method which has been used successfully in fluid flow was adopted in this work in view of its relative simplicity. The simulation was carried out for conditions wherein Rayleigh Number is in the range of 1036 and 10 and channel aspect ratio in the range of 0.03 to 0.2.Both vertical and inclined channels were treated. In the case of the inclined channel, inclination angle to the horizontal was varied between 0° and 90°. The temperature and velocity distributions obtained for each of the cases was used to compute the Nusselt Numbers. A logarithmic plot of obtained Nusselt number against Rayleigh number yielded a slope of 0.22 and an intercept of –0.37 for the vertical channel. Comparative finite element solution from literature yielded a slope of 0.26 and an intercept of –0.16. Nusselt number also increased with angle of inclination up to 90º when investigated in inclined channels Investigation of the velocity distributions along the axis of the channel showed that the fluid is faster at the top of the channel than the bottom. For channel width in the range of 0.03m to 0.05m normal dome-like parabolic velocity profiles were obtained , while widths above 0.05m had dome-like parabolic velocity profiles with the middle sagged. For all range of widths the temperature profiles are inverted parabolic.This study apart from demonstrating the applicability of the random vortex method , thus showed that maximum natural convective heat transfer occurred when the channel is vertical (i.e. angle of inclination is 90º).Keywords: Heat Transfer, Natural Convection, Simulation, Vortex Method, Channel

On the regularity of stochastic currents, fractional Brownian motion and applications to a turbulence model

We study the pathwise regularity of the map $$ \phi \mapsto I(\phi) = \int_0^T $$ where $\phi$ is a vector function on $\R^d$ belonging to some Banach space $V$, $X$ is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A \emph{stochastic current} is a continuous version of this map, seen as a random element of the topological dual of $V$. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture that those are also necessary. Next we verify the sufficient conditions when the process $X$ is a $d$-dimensional fractional Brownian motion (fBm); we identify regularity in Sobolev spaces for fBm with Hurst index $H \in (1/4,1)$. Next we provide some results about general Sobolev regularity of Brownian currents. Finally we discuss applications to a model of random vortex filaments in turbulent fluids.

Umbilic point screening in random optical fields

Umbilic points--singular points of curvature characterized by a fractional topological charge q=+/-1/2--are the most numerous of all special points in the landscape of random optical fields (speckle patterns), outnumbering maxima, minima, saddle points, and optical vortices. To the best of our knowledge, we present the first experimental evidence that positive and negative umbilic points screen one another. Theory predicts that in the absence of screening the charge variance in a bounded region is proportional to the area of the region, whereas in the presence of screening the variance is drastically reduced and is proportional to the perimeter. Our data confirm this latter prediction and provide the first estimates of the screening lengths for umbilic points of the intensity and of the amplitude (field modulus).

A correction method for measuring turbulence kinetic energy dissipation rate by PIV

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.