Anisotropic Turbulence Research Articles

The coexistence of the streaming instability and the vertical shear instability in protoplanetary disks. Scale dependence of dust diffusion

The vertical shear instability and the streaming instability are two robust sources of turbulence in protoplanetary disks. The former has been found to induce anisotropic turbulence that is stronger in the vertical than in the radial dimension and to be overall stronger compared to the largely isotropic turbulence caused by the streaming instability. In this study, we shed light on the dust diffusion by the vertical shear instability and the streaming instability separately and together, and in particular on the direction- and scale-dependence of the diffusion. To this end, we employ two-dimensional global models of the two instabilities either in isolation or in combination. The vertical shear instability in isolation diffuses dust more strongly in the vertical direction than the streaming instability in isolation, resulting in a wave-shaped dust layer in our two-dimensional simulations. Compared with this large-scale diffusion, though, our study highlights that the vertical shear instability causes substantially weaker or even negligible small-scale diffusion. We validate this result using previously published three-dimensional simulations. In particular when simulating centimetre-sized dust, the undulating dust layer becomes internally razor-thin. In contrast, the diffusion owing to the streaming instability exhibits only a marginal scale-dependence, with the dust layer possessing a Gaussian shape. In models including both instabilities, the undulating mid-plane layer is broadened to a width set by the intrinsic diffusion level caused by the streaming instability.

Turbulent anisotropy and coherent structures in flow through a symmetric compound channel with emergent floodplain vegetation

Turbulent anisotropy and coherent structures in flow through a symmetric compound channel with emergent floodplain vegetation

Decoherence of high-dimensional orbital angular momentum entanglement in anisotropic turbulence

The decoherence of high-dimensional orbital angular momentum (OAM) entanglement in the weak scintillation regime has been investigated. In this study, we simulate atmospheric turbulence by utilizing a multiple-phase screen imprinted with anisotropic non-Kolmogorov turbulence. The entanglement negativity and fidelity are introduced to quantify the entanglement of a high-dimensional OAM state. The numerical evaluation results indicate that entanglement negativity and fidelity last longer for a high-dimensional OAM state when the azimuthal mode has a lower value. Additionally, the evolution of higher-dimensional OAM entanglement is significantly influenced by OAM beam parameters and turbulence parameters. Compared to isotropic atmospheric turbulence, anisotropic turbulence has a lesser influence on high-dimensional OAM entanglement.

A mathematical model for the interaction of anisotropic turbulence with porous surfaces

Leading-edge noise is a complex phenomenon that occurs when a turbulent fluid encounters a solid object, and is a notable concern in various engineering applications. This study enhances a mathematical leading-edge noise model (Hales et al., J. Fluid Mech., vol. 970, 2023, A29) for anisotropic flow and porous boundaries. The model has two key components. First, we adjust the velocity spectrum to account for the possibility of anisotropy in the flow. This paper rigorously introduces a third dimension for the turbulence spectrum that preserves the turbulence kinetic energy and mathematical definitions for integral length scales. Second, we adapt the fully analytical acoustic transfer function to account for different boundaries by implementing convective impedance boundary conditions when formulating the gust-diffraction problem. This problem is then solved using the Wiener–Hopf technique. We discuss important aspects of this method, including the factorisation of a non-trivial scalar kernel function and the application of suitable edge conditions for the problem. Each modification is inspired by experimental leading-edge noise data using a series of different porous leading edges and anisotropic turbulence generated by a cylinder upstream of the edge. Experimental data demonstrate the interplay between anisotropy and leading-edge modifications while achieving the characteristic mid-frequency noise reduction expected from porous leading edges. Our model is adapted to best fit the trends of the data via a tailored impedance function, leading to good agreement with all datasets across an extended frequency range. This tailored function is used to successfully validate the model against other datasets from a different set of experiments.

Phase transitions in anisotropic turbulence.

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres, oceans, and stars, its manifestations can vary considerably between different physical systems. For instance, three-dimensional turbulent flows display a forward energy cascade from large to small scales, while in two-dimensional turbulence, energy cascades from small to large scales. In a given physical system, a transition between such disparate regimes of turbulence can occur when a control parameter reaches a critical value. The behavior of flows close to such transition points, which separate qualitatively distinct phases of turbulence, has been found to be unexpectedly rich. Here, we survey recent findings on such transitions in highly anisotropic turbulent fluid flows, including turbulence in thin layers and under the influence of rapid rotation. We also review recent work on transitions induced by turbulent fluctuations, such as random reversals and transitions between large-scale vortices and jets, among others. The relevance of these results and their ramifications for future investigations are discussed.

A local and global feature fusion network for Super-Resolution reconstruction of turbulent flows

The resolution of flow fields represents a significant factor influencing the accuracy of turbulent flow analysis. Nevertheless, the acquisition of high-resolution turbulence data remains a challenge due to the limitations imposed by computing resources. The interpolation method, while capable of achieving high-resolution turbulence at low cost, faces challenges in capturing details of turbulent flows. In this study, a local and global feature fusion network (LGFN) is designed for the reconstruction of high-resolution turbulent flows with high quality. First, dual parallel branches made of dense blocks are introduced into the LGFN to extract local features of turbulent flows. Moreover, the features after the first dense block of each branch are summarized into the self-attention block to obtain global features. The extracted local and global features are aggregated through learnable weight parameters to achieve feature fusion. Finally, the fused turbulence features are scaled to the same dimensional size as the high-resolution turbulence through the implementation of multilayer pixel shuffle layers and convolution layers. The effectiveness of the proposed network was evaluated using datasets of forced isotropic turbulence and channel turbulence. The results demonstrate that the reconstructed velocity fields of the LGFN exhibit the highest degree of similarity to the direct numerical simulation results, in comparison with bicubic interpolation, static convolutional neural network, and super-resolution dense connection network results. In addition, compared to alternative methods, the proposed network effectively captures the characteristics of isotropic or anisotropic turbulence even at larger scales.

Four-dimensional flow characteristics of air-entrained turbulent impinging waterjet onto quiescent water surface

This paper presents a time-resolved three-dimensional (4D) flow fields measurement of the continuous phase of a turbulent impinging jet inducing foam formation using the Lagrangian particle tracking velocimetry utilizing the Shake-The-Box algorithm. With the systems equipped with four high-speed cameras, time-series of images of fluid tracer particles were acquired. The Vortex-In-Sharp (VIC#) method was used to reconstruct the Eulerian flow fields of the particle tracks. The impinging jet was characterized as plume-like along the vertical direction with two distinct layers: developing shear and fully developed shear. The streamwise vortex structures of the continuous phase were influenced by the bubble plume motion, and the results showed high amplitude oscillations of the acceleration and deceleration near the jet source resulting in the formation of ring-like vortices, which break down as the jet moves downstream with its momentum dissipated. The flow of the continuous phase of impinging jet was self-similar both at the developed shear layer and the fully developed diffusion layer beneath the water pool and is characterized as homogeneous shear flow with anisotropy turbulence. The classical assumption of self-similarity with Gaussian profiles for continuous phase velocity is verified experimentally. We found that the results show a huge potential of blue energy harvesting from the low frequency (∼2 Hz) dissipating kinetic energy of the turbulent plume-like jet underneath the impinging water surface using triboelectric nanogenerator.

Turbulent Flow and Wall Forces in Staggered Square Cylinder Porous Media: An Large Eddy Simulation Analysis

Abstract The wall-modeled-large eddy simulation (WMLES) technique was used to analyze turbulent flow in a porous medium composed of a staggered arrangement of square cylinders. The study focused on a porosity range of 0.3–0.8 at a pore Reynolds number of 104. The research provides novel information on pressure and shear force distributions around the cylinders and time-averaged values of particle drag and fluctuating lift coefficients. Results indicate that flow physics are mainly driven by an expansion region in front of the central particle and another one in the rear, where the flow is contracted and strongly accelerated. In the first region, velocities, turbulence kinetic energy (k), and its dissipation rate (ε) are attenuated by a sudden pressure increase, while in the contraction region, the effect is the opposite. As porosity decreases, flow gradients and the overall levels of k, ε, and normalized Reynolds stresses become more significant. Turbulent anisotropy increases as porosity decreases below 0.6. Hydrodynamic stresses in the last interval present relatively uniform levels, which is a unique feature that may be considered in designing dedicated engineering devices with controlled stresses.

The influence of the shock-to-reshock time on the Richtmyer–Meshkov instability in reshock

Experiments on the Richtmyer–Meshkov instability (RMI) in a dual driver vertical shock tube (DDVST) are described. An initially planar, stably stratified membraneless interface is formed by flowing air from above and sulfur hexafluoride from below the interface location using the method of Jones & Jacobs (Phys. Fluids, vol. 9, issue 1997, 1997, pp. 3078–3085). A random three-dimensional, multi-modal initial perturbation is imposed by vertically oscillating the gas column to produce Faraday waves. The DDVST design generates two shock waves, one originating above and one below the interface, with these shocks having independently controllable strengths and interface arrival times. The shock waves have nominal strengths of $M_L=1.17$ and $M_H=1.18$ for the shock wave originating in the light and heavy gas, respectively, with these strengths chosen to result in arrested bulk interface motion following reshock. The influence of the length of the shock-to-reshock time, as well as the order of shock arrival, on the post-reshock RMI is examined. The mixing layer width grows according to $h\propto t^\theta$ , where $\theta _H=0.36\pm 0.018$ (95 %) and $\theta _L=0.38\pm 0.02$ (95 %) for heavy and light shock first experiments, respectively, indicating no strong dependence on the order of shock wave arrival. Volume integrated specific turbulent kinetic energy (TKE) in the mixing layer versus time is found to decay according to $E_{tot}/\bar {\rho }\propto t^p$ with $p_H=-0.823\pm 0.06$ (95 %) and $p_L=-1.061\pm 0.032$ (95 %) for heavy and light shock first experiments, respectively. Notably, the 95 % confidence intervals do not overlap. Analysis on the influence of the shock-to-reshock time on turbulent length scales, transition criteria, spectra and mixing layer anisotropy are also presented.

Propagation of Sine hyperbolic Gaussian vortex beam (ShGvB) in vertical anisotropic oceanic turbulence with adaptive optics correction

The propagation of Sinh Gaussian vortex beam (ShGvB) along vertical anisotropic oceanic turbulence is established using the spatial power spectrum which depends upon the depth of the ocean. The average intensity of the beams has been derived. For 100 m depth, the average intensity has been plotted and studied using the measured salinity and temperature from the ocean in both isotropic and anisotropic oceanic turbulence systems. The average transmittance of the ShGvB is studied and found that the beam degrades faster in anisotropic media than in isotropic media. To mitigate the aberrations adaptive optics (AO) correction is incorporated in the study along the vertical link. Quantitative estimates of the Bit error rate (BER) have been made to evaluate the beam's performance for vertical underwater optical communication and found that by improving the signal-to-noise ratio and incorporating AO, the ShGvB performs effectively in vertical underwater optical communication.

The isolated effect of yield stress in viscoplastic turbulent flow

Turbulent flows of viscoplastic fluids are present in several industrial and natural applications. The effects of yield stress on this problem have always been studied as a part of a larger physical context, because real viscoplastic materials have many properties that cannot be easily isolated. Direct numerical simulations have recently emerged as a viable tool for investigating non-Newtonian fluid flow in turbulent regimes. In the present work, we solve the turbulent flow of an ideal Bingham fluid, focusing on the isolated effect of yield stress. A numerical scheme for viscoplastic flows was implemented based on the lattice Boltzmann method. An outstanding characteristic of this scheme is the possibility of representing infinite viscosity by setting the relaxation frequency to zero, enabling the representation of the Bingham constitutive equation without artifacts, and producing a more accurate representation of the yield surfaces. In the turbulent channel flow simulations, the friction Reynolds number was fixed at 180, while the Bingham number varied from 0 (Newtonian) to 0.15. It is shown that unyielded portions of material travel along with the flow near the centerline. These unyielded spots do not disappear quickly, but rather have a significant lifetime. Another interesting outcome is that the yield stress increases the turbulence anisotropy, by lowering the spanwise and normal velocity fluctuations, while the streamwise component becomes higher. Reynolds stresses and budgets of turbulent kinetic energy have been analyzed regarding the increased bulk velocities that were found by increasing the yield stress.

Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales

Abstract. The deterministic motions of clouds and turbulence, despite their chaotic nature, have nonetheless been shown to follow simple statistical power-law scalings: a fractal dimension D relates individual cloud perimeters p to a measurement resolution, and turbulent fluctuations scale with the air parcel separation distance through the Hurst exponent, ℋ. However, it remains uncertain whether atmospheric turbulence is best characterized by a split isotropy that is three-dimensional (3D) with H=1/3 at small scales and two-dimensional (2D) with ℋ=1 at large scales or by a wide-range anisotropic scaling with an intermediate value of ℋ. Here, we introduce an “ensemble fractal dimension” De – analogous to D – that relates the total cloud perimeter per domain area 𝒫 as seen from space to the measurement resolution, and we show theoretically how turbulent dimensionality and cloud edge geometry can be linked through H=De-1. Observationally and numerically, we find the scaling De∼5/3 or H∼2/3, spanning 5 orders of magnitude of scale. Remarkably, the same scaling relationship links two “limiting case” estimates of 𝒫 evaluated at resolutions corresponding to the planetary scale and the Kolmogorov microscale, which span 10 orders of magnitude. Our results are nearly consistent with a previously proposed “23/9D” anisotropic turbulent scaling and suggest that the geometric characteristics of clouds and turbulence in the atmosphere can be easily tied to well-known planetary physical parameters.

Turbulent flow structures and Reynolds stress anisotropy in an asymmetric sinuous mobile channel

Turbulent flow structures and Reynolds stress anisotropy in an asymmetric sinuous mobile channel

Performance analysis of Sinh and Cosh Gaussian vortex beam in vertical underwater optical communication

The performance analysis of Sinh Gaussian vortex beam (ShGvB) and Cosh Gaussian vortex beam (ChGvB) in oceanic turbulence is established by employing an anisotropic spatial power spectrum that considers the influence of the ocean depth to mimic the actual oceanic conditions. Since the salinity and temperature variations along depth are not linear, the actual data of temperature and salinity measured from the tropical region of the ocean is used for the current study. The propagation properties of the ShGvB are studied by deriving the cross-spectral density of the beam, and the average intensity of the beam is plotted over depth and studied in both isotropic and anisotropic oceanic turbulence systems. The analysis of the beam spot radius shows that the beam degrades faster in anisotropic media than in isotropic media. Quantitative estimation of the detection probability, channel capacity and bit error rate (BER) have been made to evaluate the beam's performance for vertical underwater optical communication. The BER may be improved by enlarging the detector aperture radius and signal-to-noise ratio. The ShGvB performs effectively in vertical underwater optical communication compared to the ChGvB.

Settling velocity characteristics of inertial particles in turbulent and wave-induced environments

In the present study, a theoretical model is proposed to calculate the settling velocity of solid particles in turbulence generated by both oscillatory and nearly horizontal flow motions. In contrast to other previous models that typically compartmentalize two flow conditions in their studies, this study takes a more comprehensive approach by considering the combined effects of both conditions. Taking into account the influence of drag nonlinearity, virtual mass and Basset history forces, the new theoretical model is formulated. The proposed model is obtained by solving the particle motion in fluid flow under some reasonable assumptions. Accordingly, we obtain a new dimensionless term to better take into account the effect of turbulence anisotropy on the settling velocity and the role of the sediment damping coefficient. Application of this term for other conditions is discussed in the paper. The present model shows satisfactory agreement with a wide range of experimental and numerical data and with different flow conditions found in the existing literature. These data include homogeneous isotropic turbulence with high resolution direct numerical simulations (DNS), turbulent open channel and vertical oscillation.

Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence

Various active materials exhibit strong spatio-temporal variability of their orientational order known as active turbulence, characterised by irregular and chaotic motion of topological defects, including colloidal suspensions, biofilaments, and bacterial colonies.In particular in three dimensions, it has not yet been explored how active turbulence responds to changes in material parameters and chirality.Here, we present a numerical study of three-dimensional (3D) active nematic turbulence, examining the influence of main material constants: (i) the flow-alignment viscosity, (ii) the magnitude and anisotropy of elastic deformation modes (elastic constants), and (iii) the chirality. Specifically, this main parameter space covers contractile or extensile, flow-aligning or flow tumbling, chiral or achiral elastically anisotropic active nematic fluids. The results are presented using time- and space-averaged fields of defect density and mean square velocity. The results also discuss defect density and mean square velocity as possible effective order parameters in chiral active nematics, distinguishing two chiral nematic states—active nematic blue phase and chiral active turbulence. This research contributes to the understanding of active turbulence, providing a numerical main phase space parameter sweep to help guide future experimental design and use of active materials.

BxC Toolkit: Generating Tailored Turbulent 3D Magnetic Fields

Turbulent states are ubiquitous in plasmas, and the understanding of turbulence is fundamental in modern astrophysics. Numerical simulations, which are the state-of-the-art approach to the study of turbulence, require substantial computing resources. Recently, attention shifted to methods for generating synthetic turbulent magnetic fields, affordably creating fields with parameter-controlled characteristic features of turbulence. In this context, the BxC toolkit was developed and validated against direct numerical simulations (DNSs) of isotropic turbulent magnetic fields. Here, we demonstrate novel extensions of BxC to generate realistic turbulent magnetic fields in a fast, controlled, geometric approach. First, we perform a parameter study to determine quantitative relations between the BxC input parameters and the desired characteristic features of the turbulent power spectrum, such as the extent of the inertial range, its spectral slope, and the injection and dissipation scale. Second, we introduce in the model a set of structured background magnetic fields, B 0, as a natural and more realistic extension to the purely isotropic turbulent fields. Third, we extend the model to include anisotropic turbulence properties in the generated fields. With all these extensions combined, our tool can quickly generate any desired structured magnetic field with controlled, anisotropic turbulent fluctuations, faster by orders of magnitude with respect to DNSs. These can be used, e.g., to provide initial conditions for DNSs or easily generate synthetic data for many astrophysical settings, all at otherwise unaffordable resolutions.

Anisotropic turbulence modeling for natural channel flow: A numerical approach with finite element method

In this study, we propose a numerical model aimed at improving the understanding and prediction of flow velocities in natural channels. This model specifically focuses on the challenges presented by anisotropic turbulence and bottom roughness. By incorporating the mixing length concept into an algebraic turbulence model and employing the finite element method with Streamline-Upwind/Petrov–Galerkin (SUPG) stabilization, our model seeks to refine the simulation of axial velocity distribution and secondary motions. Validation was achieved through Acoustic Doppler Current Profiler (ADCP) measurements in three sections of the Canal do Rodeador, showing our model’s predictions of discharge and average velocity to have a deviation of approximately 9.34% from experimental data. The results underline the significance of secondary currents and turbulence anisotropy in shaping channel flow behaviors, offering new insights into the interactions between flow characteristics and channel bed features. This model stands out as a robust tool for hydraulic structure design and hydrokinetic potential evaluation, providing a non-intrusive, cost-effective alternative to traditional methods.

Fluctuation-induced transitions in anisotropic two-dimensional turbulence

Fluctuation-induced transitions in anisotropic two-dimensional turbulence