Turbulent Fluid Motion Research Articles

Filaments in and between galaxy clusters at low and mid-frequency with the SKA

Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50-350\,MHz and 950-1760\,MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARay 2.0 and the MeerKAT+ telescope. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediate-frequency radio telescopes make them the favourite instruments for the study these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

Turbulence, thermal pressure, and their dynamical effects on cosmic baryonic fluid

ABSTRACT We employ the IllustrisTNG simulation data to investigate the turbulent and thermal motions of the cosmic baryonic fluid. With continuous wavelet transform techniques, we define the pressure spectra, or density-weighted velocity power spectra, as well as the spectral ratios, for both turbulent and thermal motions. We find that the magnitude of the turbulent pressure spectrum grows slightly from $z=4$ to 2 and increases significantly from $z=2$ to 1 at large scales, suggesting progressive turbulence injection into the cosmic fluid, whereas from $z=1$ to 0, the spectrum remains nearly constant, indicating that turbulence may be balanced by energy transfer and dissipation. The magnitude of the turbulent pressure spectra also increases with environmental density, with the highest density regions showing a turbulent pressure up to six times that of thermal pressure. We also explore the dynamical effects of turbulence and thermal motions, discovering that while thermal pressure provides support against structure collapse, turbulent pressure almost counteracts this support, challenging the common belief that turbulent pressure supports gas against overcooling.

Exploring the impact of compressibility on reconstructed porous materials: A numerical study

This study underscores fluid density's significance in CFD simulations for porous materials, addressing its impact on accuracy and computational efficiency. The paper proposes a tailored form of Navier-Stokes equations that accounts for fluid density's influence on CFD analyses of porous materials in industrial contexts, including cases where the solid phase is deformable. Numerical analyses demonstrate fluid density's significance (ρ≠constant) and explore the importance of the energy equation in governing equations. The energy equation is essential in setting up the governing equations, as it calculates thermal characteristic length based on cell temperatures. By examining various porous material samples, the study suggests a streamlined approach: employing a single coupled CFD-FEM simulation to directly determine each geometrical parameter. Additionally, the study investigates the capability to accurately simulate turbulent fluid motion at the pore scale and analyze the flow field characterization within porous media. Computational cost analyses underscore the advantages of coupled simulations, establishing their profitability over separate parameter-specific simulations.

Generalized scaling laws for the irrotational motions bordering a turbulent region.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_{2} much bigger than the integral scale L in the nearby turbulent region (x_{2}≫L), the variance of the velocity fluctuations 〈u_{i}^{2}〉 (i=1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k)∼k^{n} [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n=4 (Batchelor turbulence) and n=2 (Saffman turbulence) have been previously derived, with 〈u_{i}^{2}〉∼x_{2}^{-4} and 〈u_{i}^{2}〉∼x_{2}^{-3}, for n=4 and n=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], we extend these results by including any other value of n. In particular, we obtain 〈u_{i}^{2}〉∼x_{2}^{-2} and 〈u_{i}^{2}〉∼x_{2}^{-4}, for n=1 and n≥5, respectively, while n=3 yields 〈u_{i}^{2}〉∼x_{2}^{-4}ln(x_{2}). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

Identifying some regularities of the turbulent steady-state plane-parallel motion of incompressible fluid at the entrance length

This paper investigates the structural changes in the turbulent motion of an incompressible fluid in the hydrodynamic entrance region of plane-parallel pressure motion. Movement in pressure hydromechanical systems usually occurs in a turbulent regime. Studying the patterns of changes in hydrodynamic parameters under conditions of stationary turbulent pressure motion in the inlet region is a very urgent task. The study was carried out on the basis of boundary layer equations. Taking into account the dependence of changes in the kinematic viscosity coefficient that occur between layers of fluid, a boundary value problem was formed. Analytical solutions have been obtained that make it possible to obtain patterns of changes in velocity and pressure in any effective flow section. Based on the general conclusions of the study, solutions were found for two cases: a) the velocity of the fluid entering the cylindrical pipe is constant; b) the velocity of the incoming fluid has a parabolic distribution. For these cases, using computer analysis of the data obtained, general graphs of velocity changes were constructed in various sections along the hydrodynamic entrance region. These graphs, which display the change in velocity along the entire length of the inlet, make it possible to obtain the velocity of fluid movement at any point along the inlet length and estimate the length of the transition zone. The results obtained are among the least studied issues of classical fluid mechanics and are of important theoretical interest. The results obtained are applicable for the correct construction of the hydrodynamic entrance region of machinery. A calculation formula has been obtained to determine the length of the hydrodynamic inlet region

Effect of fluid motions on finite spheres released in turbulent boundary layers

This paper extends the work in Tee et al. (Intl J. Multiphase Flow, vol. 133, 2020, 103462) to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with $Re_\tau =670$ and 1300 ( $d^+=56$ and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise–spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast- and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.

Amplification and Dissipation of Magnetic Fields in Accreting Compact Objects

Magnetic fields play a crucial role in shaping the dynamics of accreting compact objects. Whether we consider the formation of a proto-neutron star during the gravitational collapse of a massive star or the accretion disk around a black hole after a compact binary merger, a key process that remains challenging to include in large-scale simulations is the amplification and dissipation of magnetic fields driven by turbulent fluid motions. Despite the enormous increase in computational power currently available, the large separation between all the relevant spatial and temporal scales still poses severe limits to what can be achieved with ideal fluid simulations. One way to tackle such issue is to rely on sub-grid models, which however need to be appropriately tuned in light of models probing the small-scale dynamics. In this work we present the current state-of-the-art of dynamo models in proto-neutron stars, which aim at describing the amplification of magnetar-like magnetic fields during the gravitational collapse of a massive star. We also review some of the works from the past few years that included turbulent dynamos in accretion disks around a black holes, relying on a mean-field formalism. Finally, we will present a recent study on polar jets with explicit turbulent resistivity which showcases the importance of employing highly accurate numerical schemes.

Spontaneous Stochasticity Amplifies Even Thermal Noise to the Largest Scales of Turbulence in a Few Eddy Turnover Times.

How predictable are turbulent flows? Here, we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the nonuniqueness of the solutions to the Euler equation that is conjectured to occur in Navier-Stokes turbulence at high Reynolds numbers, leads to universal statistics at finite times, not just at infinite time as for standard chaos. These universal statistics are predictable, even though individual flow realizations are not. Any small-scale noise vanishing slowly enough with increasing Reynolds number can trigger spontaneous stochasticity, and here we show that thermal noise alone, in the absence of any larger disturbances, would suffice. If confirmed for Navier-Stokes turbulence, our findings would imply that intrinsic stochasticity of turbulent fluid motions at all scales can be triggered even by unavoidable molecular noise, with implications for modeling in engineering, climate, astrophysics, and cosmology.

Data-based approach for time-correlated closures of turbulence models.

Developed turbulent motion of fluid still lacks an analytical description despite more than a century of active research. Nowadays, phenomenological ideas are widely used in practical applications, such as small-scale closures for numerical simulations of turbulent flows. In the present paper, we use a shell model of turbulence to construct a closure intended to have a solid theoretical background and to capture intrinsic probabilistic features of turbulence. Shell models of turbulence are dynamical deterministic systems used to model energy cascade and other key aspects of the Navier-Stokes such as intermittency. We rescale the variables of the Sabra model in a way which leads to hidden symmetries and universal distributions. We then use such fine distributions to write closures, i.e., missing expressions for some of the Sabra variables. Our closures rely on approximating probability density functions using a Gaussian mixture model, which makes them probabilistic by nature and allows us to write time-correlated closures. We also provide a framework where other machine learning tools can be employed with reduced black-box aspects.

Velocity distribution and hydrodynamic drag in turbulent flow

This work aims to study the vertical velocity distribution in the near-wall layer of a pipe, channel, and boundary layer of a flat plate because these issues are of great practical and theoretical importance. Until now, engineering calculations of turbulent flows have been based on empirical formulas derived in the last century. The theory of turbulent fluid motion has not been completed, and the issues of velocity distribution and hydraulic resistance remain open for further study. It is known that velocity distribution in the flow is intricately linked to hydraulic resistance. Therefore, the study’s objectives also include determining the position of the point of maximum turbulent tangential stresses and comparing the change in tangential stresses with the logarithmic velocity profile. Based on calculation and analytical methods, we have researched the distribution of the turbulent component of the tangential stress along the depth of the flow. Derived an expression determining the position of the maximum point of the turbulent component of the tangential stress for smooth tubes. The contribution of the viscous component of the tangential stress at different points along the flow depth has been evaluated. The calculation results determining the position of the maximum point of the turbulent component of the tangential stress were compared with experimental data on velocity distribution in the flow. With the decrease of the hydraulic resistance coefficient, the point of maximum turbulent tangential stresses shifts towards the solid flow boundary. Based on the results of comparing the maximum turbulent tangential stresses with the total tangential stress, we can conclude that the contribution of the viscous component of the tangential stress to the total amount of friction and its influence on velocity distribution is significant. The angular coefficient of the velocity profile for the flow core is determined.

Acoustic Response of a Vibrating Elongated Cylinder in a Hydrodynamic Turbulent Flow

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.

Simulating Slosh Induced Damping, with Application to Aircraft Wing-like Structures

The added damping generated by liquid sloshing in a tank has been utilized in a number of civil applications, including aviation, to reduce the vibration of the system. As part of a wider EU H2020 project called SLOWD (Sloshing Wing Dynamics), the presented study performed numerical simulations on the slosh-induced damping of liquid in tanks that were under free decay oscillations and embedded in an aircraft wing-like structure. A new open-source partitioned fluid–structure interaction software framework is presented and employed for the numerical simulations. Periodic sloshing waves and violent vertical fluid motions are observed in the study. These demonstrate the effects of slosh-induced damping under different excitation amplitudes of the structure and a varying number of baffled regions within the tank. Various sloshing patterns caused by different combinations of the excitation amplitude and compartment numbers lead to different induced dampings of the free decay motion. We observed a distinctly non-monotonic function on the slosh damping when the initial excitation amplitude is small (i.e., 0.25), with a 59% reduction when we increase the number of baffled compartments from one to four, and a 153% increase when moving from one to eight compartments. This is due to the change in the sloshing wave frequency, resulting in a significant change in the impact of the fluid between the tank ceiling and the wave crests. When the initial excitation amplitude is large (i.e., 1.0), there is no significant change in the slosh-induced damping when changing the number of compartments in the tank, for the range of parameters considered, due to the highly turbulent fluid motion. This work is expected to form the basis of further, more detailed studies within the context of the SLOWD project and its ever-expanding experimental data output.

A Hydrodynamic Analog of the Casimir Effect in Wave-Driven Turbulent Flows

We present experimental results on a fluctuation-induced force observed in Faraday wave-driven turbulence. As recently reported, a long-range attraction force arises between two walls that confine the wave-driven turbulent flow. In the Faraday waves system, the turbulent fluid motion is coupled with the disordered wave motion. This study describes the emergence of the fluctuation-induced force from the viewpoint of the wave dynamics. The wave amplitude is unaffected by the confinement while the wave erratic motion is. As the wall spacing decreases, the wave motion becomes less energetic and more anisotropic in the cavity formed by the walls, giving rise to a stronger attraction. These results clarify why the modelling of the attraction force in this system cannot be based on the wave amplitude but has to be built upon the wave-fluid motion coupling. When the wall spacing is comparable to the wavelength, an intermittent wave resonance is observed, and it leads to a complex short-range interaction. These results contribute to the study of aggregation processes in the presence of turbulence and its related problems such as the accumulation of plastic debris in coastal marine ecosystems or the modelling of planetary formation.

Interface topology and evolution of particle patterns on deformable drops in turbulence

The capture of neutrally buoyant, sub-Kolmogorov particles at the interface of deformable drops in turbulent flow and the subsequent evolution of particle surface distribution are investigated. Direct numerical simulation of turbulence, phase-field modelling of the drop interface dynamics and Lagrangian particle tracking are used. Particle distribution is obtained considering excluded-volume interactions, i.e. by enforcing particle collisions. Particles are initially dispersed in the carrier flow and are driven in time towards the surface of the drops by jet-like turbulent fluid motions. Once captured by the interfacial forces, particles disperse on the surface. Excluded-volume interactions bring particles into long-term trapping regions where the average surface velocity divergence sampled by the particles is zero. These regions correlate well with portions of the interface characterized by higher-than-mean curvature, indicating that modifications of the surface tension induced by the presence of very small particles will be stronger in the highly convex regions of the interface.

Power-law generalization of Newton’s formula for shear stress in a liquid in the form of a tensor rheological relation

A generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form and the corresponding rheological relation is written in tensor form. Depending on the exponent in this rheological ratio, one can come to a description of either a laminar or turbulent flow regime. In the latter case, there is a system of differential equations with the no-slip boundary condition. The proposed system of equations for turbulent fluid motion can be useful, at least, for obtaining preliminary, estimated characteristics of turbulent flow before starting numerical modeling using modern differential turbulence models. For some values of the exponent, this system can be used to describe the behavior of power-law fluids, as well as fluids with small additives of polymers in the manifestation of the Toms effect.

Comparison and validation of various turbulence models for U-bend flow with a magnetic resonance velocimetry experiment

Turbulence modeling plays an important role in the accurate prediction of turbulent fluid motion in computational fluid dynamics simulations using the Reynolds-averaged Navier–Stokes equations. A new one-equation Wray–Agarwal (WA) turbulence model has recently been developed by the present authors to improve the prediction of nonequilibrium turbulent flows with large separation and curvature. In this paper, the WA turbulence model is employed to simulate the internal turbulent flow characteristics in a U-bend, and the computed results are compared with experimental data. The results obtained from four other commonly used turbulence models, viz., the one-equation Spalart–Allmaras, two-equation standard k-ε, renormalization group k-ε, and shear stress transport k-ω models, are also compared. Detailed experimental data are obtained using magnetic resonance velocimetry. The results computed with the five different turbulence models show that the WA turbulence model gives the highest accuracy in predicting the complex three-dimensional turbulent characteristics of flow with large curvature in a U-bend.

Modeling of a dynamic discrete cellular system

Cellular automata have found application in the study of discrete dynamic processes of physical reality. The article deals with the evolution of a discrete dynamic cellular system modeled in the Wolfram Mathematica computer environment. A comparative analysis of various variants of the cellular automaton model implementation is given: according to rules 90, 105 and 110. An algorithm for modeling the deformed state of a solid body using rule 110 is proposed. To simulate local structures that simulate stress concentrators, the algorithm is supplemented by generating a sequence of pseudo-random numbers. The simulation results showed that the appearance of stress concentrators corresponds to the transition from deterministic to chaotic behavior of a discrete cellular system. The article also estimates the possibility of using a discrete cellular system to simulate the turbulent motion of an incompressible fluid based on a generalized local balance model. The appearance of turbulence zones can be estimated by changing the pattern of the cellular automaton.

Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation

The Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher’s equation. A detailed understanding of the large time behaviour of the solutions to these equations has been mostly achieved in the case where the relaxation function, measuring the intensity of the relaxation towards equally distributed velocity densities, is constant. The goal of the presented work is to provide a general method to tackle the question of convergence to equilibrium when the relaxation function is not constant, and to do so as quantitatively as possible. In contrast to the usual modal decomposition of the equations, which is natural when the relaxation function is constant, we define a new Lyapunov functional of pseudodifferential nature, one that is motivated by the modal analysis in the constant case, that is able to deal with full spatial dependency of the relaxation function. The approach we develop is robust enough that one can apply it to multi-velocity Goldstein-Taylor models, and achieve explicit rates of convergence. The convergence rate we find, however, is not optimal, as we show by comparing our result to those found in [8].

A Visualization Framework for Multi-scale Coherent Structures in Taylor-Couette Turbulence.

Taylor-Couette flow (TCF) is the turbulent fluid motion created between two concentric and independently rotating cylinders. It has been heavily researched in fluid mechanics thanks to the various nonlinear dynamical phenomena that are exhibited in the flow. As many dense coherent structures overlap each other in TCF, it is challenging to isolate and visualize them, especially when the cylinder rotation ratio is changing. Previous approaches rely on 2D cross sections to study TCF due to its simplicity, which cannot provide the complete information of TCF. In the meantime, standard visualization techniques, such as volume rendering / iso-surfacing of certain attributes and the placement of integral curves/surfaces, usually produce cluttered visualization. To address this challenge and to support domain experts in the analysis of TCF, we developed a visualization framework to separate large-scale structures from the dense, small-scale structures and provide an effective visual representation of these structures. Instead of using a single physical attribute as the standard approach which cannot efficiently separate structures in different scales for TCF, we adapt the feature level-set method to combine multiple attributes and use them as a filter to separate large- and small-scale structures. To visualize these structures, we apply the iso-surface extraction on the kernel density estimate of the distance field generated from the feature level-set. The proposed methods successfully reveal 3D large-scale coherent structures of TCF with different control parameter settings, which are difficult to achieve with the conventional methods.

Generation and sustenance of electric fields in sandstorms

Sandstorms are frequently accompanied by the generation of intense electric fields and lightning. In a very narrow region close to the ground level, sand particles undergo a charge exchange mechanism whereby larger (resp. smaller) sized sand grains become positively (resp. negatively) charged are then entrained by the turbulent fluid motion. Our central hypothesis is that differently sized sand particles get differentially transported by the turbulent flow resulting in a large-scale charge separation, and hence a large-scale electric field. We utilize our simulation framework, comprising of large-eddy simulation of the turbulent atmospheric boundary layer along with sand particle transport and an electrostatic Poisson solver, to investigate the physics of electric fields in sandstorms and thus, to confirm our hypothesis. We utilize the simulation framework to investigate electric fields in weak to strong sandstorms that are characterized by the number density of the sand particles. Our simulations reproduce observational measurements of both mean and RMS fluctuation values of the electric field. We propose a scaling law in which the electric field scales as the two-thirds power of the number density that holds for weak-to-medium sandstorms.