Anisotropic Turbulence Research Articles

Evidence for layered anisotropic stratified turbulence in a freely evolving horizontal shear flow

We present evidence for layered anisotropic stratified turbulence (LAST) and mixing produced in a freely evolving uniformly stratified shear layer where the direction of shear is orthogonal to gravity. As originally reported by Basak & Sarkar (J. Fluid. Mech., vol. 568, 2006, pp. 19–54), such a flow develops a rich three-dimensional structure in the form of interlocking columnar vortices formed by horizontal shear instability that remain coherent at large scales due to the stabilising vertical stratification. Here, we modify the initial velocity field by introducing additional small-amplitude vertical perturbations designed to be representative of pre-existing horizontal layers often observed in strongly stratified ocean environments. This reveals a novel finite amplitude, non-normal mode growth mechanism through which the vertical shear between layers may be rapidly amplified by its interaction with the horizontal shear layer prior to the growth of shear instability, leading to a rapid turbulent transition instigated by the subsequent interaction of the layers with the emerging columnar vortices. Through a consideration of relevant flow statistics and associated dimensionless parameters, we demonstrate that turbulence can enter the LAST regime, thereby indicating a generic mechanism leading to the transient development of regions of strongly stratified turbulence in the ocean. We discuss the properties of mixing and the parameterisation of mixing efficiency in terms of the relationship between turbulent length scales in the flow, in particular highlighting links to models based on the classical vertical shear instability paradigm typically associated with more weakly stratified flows that produce isolated turbulent ‘patches’.

Anisotropic turbulence modeling of the atmospheric surface layer: Validation of novel model settings and comparison with traditional two-equation models in flows over complex terrain

For atmospheric flows, the limitations of the eddy viscosity assumption are even more critical in cases involving complex terrain and features, where secondary strains are influential. Reynolds Stress Models (RSMs) can account for these effects, but their numerical stiffness and crucially the lack of established guidelines for modelers regarding the appropriate boundary conditions and model settings, as exist for eddy-viscosity models (EVMs), have led to limited adoption. In order to circumvent the shortcomings of EVMs, the focus has been directed at large eddy simulations (LES), which have greater computational requirements that can be prohibitive. Thus, this work aims to extend the traditional methodology that has been applied to adapt EVMs to atmospheric flows to an RSM that incorporates near-ground effects. This results in suggestions for new model constants and novel boundary conditions, which can easily be adapted according to local atmospheric parameters and employed by modelers. The performance of the proposed RSM is compared with four distinct EVMs through real-life cases representing two distinct complex terrain configurations. The results showed that the RSM indeed outperformed the EVMs, and it was found that only its anisotropic formulation could capture more complex flow features that were observed experimentally.

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Aerodynamic investigation of the turbulent flow past a louvered-fin-and-tube automotive heat exchanger

Turbulent flow past a radiator contributes to noise emission when interacting with a downstream cooling fan. This study examines turbulent flow characteristics downstream of a radiator, focusing on turbulence production, dissipation, non-homogeneity, and anisotropy. We assess turbulence models based on isotropy and homogeneity for noise prediction in real applications. Results show significant non-homogeneity due to the radiator grid’s wakes, extending downstream to a region where the fan would be located. Flow in this region trends toward isotropy, especially when considering a downstream circularly-holed wood panel mimicking the flow contraction caused by a fan casing. The radiator core’s fins and louvers break down vortical structures more than generating large eddies, as reported in studies involving heat exchangers with larger gaps between cooling pipes. The von Kármán turbulence model approximates the experimental spectrum, but caution is needed with rapid flow acceleration. This investigation enhances our understanding of turbulence characteristics in the vicinity of radiators with implications for noise spectrum prediction and modeling in such systems.

Anisotropic turbulence of dense and dilute phases of particles in fluidized risers characterized using four-way coupled second-order moment method

The gas-particle flow in a fluidized bed is characterized as a “core-annulus” pattern with transient clusters moving along the circulating fluidized bed riser. These clusters exist as regions with a higher concentration of particles and are surrounded by dispersed particles at lower concentrations. In this study, fluid dynamics of both the clusters and dispersed particles suspended in the risers were investigated using the four-way coupled second-order moment method of the fluid–particle Eulerian–Eulerian two-fluid model. In the simulation, the anisotropic turbulence of either phase in the clusters and dispersed particles was studied in the risers. According to the turbulence intensities of both phases, the gas-particle flow in the fluidized riser was classified into six zones, the wall effect, cluster edge, cluster rising, cluster falling, and transient zone between the cluster rising and falling zones. As the volume fraction of the particles increased, the anisotropic ratios of the turbulence intensities in both phases increased in the dispersed zone and decreased in the cluster zone, respectively.

An investigation of the effect of stratification stability and saltation sand flux on the anisotropy of atmospheric surface layer wall turbulence

In the atmospheric surface layer (ASL), the anisotropic characteristics of turbulence become more complex due to the strong influence of heat flux and particle motion. In this paper, the effects of stratification stability and total saltation sand flux on turbulent anisotropy of ASL wall turbulence are systematically analyzed by using high-frequency 3D velocity, temperature, and saltation sand flux measured in the field. Our results show that the temperature gradient intensifies the spanwise turbulent motion and enhances the vertical motion asymmetry. Although the buoyancy-driven turbulence enhances the spanwise variation, the momentum transfer mode between the streamwise–vertical and spanwise–vertical does not change. With the increase in instability, the large-scale motions (LSM) of the spanwise velocity may be destroyed and more spanwise small-scale motions (SSM) formed. In addition, saltation increases the sharpness, randomness, and extreme frequency of spanwise velocity distribution, but does not change the momentum transfer mode. Saltation may enlarge the fluctuation range and scale of the spanwise velocity, but may not be the main factor affecting the anisotropy of SSM. These results can deepen people's understanding of wind-blown sand movement and turbulence properties in ASL, and provides empirical data and insights that can significantly contribute to the development and refinement of turbulence models, particularly those that need to account for the complex interplay between stratification stability, saltation sand flux, and turbulence anisotropy.

Analysis and Modeling of Turbulence Anisotropy of a Swirled Hot Streak Flow

Abstract This study is carried out in the context of hot streak flows in high-pressure turbines, for which a correct prediction of the temperature evolution is required. The present work particularly focuses on the turbulence anisotropy analysis of a swirled hot streak flow in a bent channel representative of a nozzle guide vane (NGV) passage of a high-pressure turbine. Large-eddy simulations are conducted with the in-house solver IC3 in order to measure and characterize the anisotropy of turbulence. Moreover, to evaluate turbulence modeling, steady simulations of the bent channel are performed with the elsA software, which solves the Reynolds-averaged Navier–Stokes (RANS) equations. LES is first used to complete a turbulent kinetic energy (TKE) budget that enables to understand the energetic transfers associated with turbulence. This budget reveals two distinct zones where turbulence activity is impacted when the curvature is reached. The analysis of the anisotropy of turbulence based on two metrics highlights a misalignment of the Reynolds stress tensor and the mean strain-rate tensor (Schmitt's criterion), and a strong anisotropy developing inside the bent duct (Lumley's analysis) that may cause the failure of the classical RANS turbulence models based on Boussinesq's hypothesis. To check this hypothesis, RANS is positioned against LES with different turbulence models that accounts or not for the anisotropy of turbulence. Both turbulence activity (TKE budgets, Lumley's analysis) and aerothermal fields (radial distributions) are compared. Results show that Explicit Algebraic Reynolds Turbulence Models (EARSM) enable to better account for the anisotropy of turbulence, which in turn promote a better prediction of temperature, both in terms of intensity and trajectory.

Direct numerical simulation of a pressurized thermal shock scenario at higher reynolds number

Direct Numerical Simulation (DNS) is performed for a pressurized thermal shock scenario in a reactor downcomer geometry. In the present work, a simplified representative geometry is adopted where cold fluid injected from a square duct is injected in a planar downcomer. A secondary hot inlet at the top of the downcomer is employed to enforce a downward flow of the injected emergency core cooling water, to mimic the effect of density driven flow. The Reynolds number of the impinging flow, based on bulk velocity and duct height, equals 12,500, while a unity Prandtl number fluid is used. The simulation is performed for two thermal boundary conditions, namely an isotemperature condition and an adiabatic condition, representing the two extreme scenarios of a conjugate heat transfer problem. The instantaneous and mean fields are first analysed in order to study the flow pattern and formation of vortical structures within the downcomer. The impinging flow is deflected radially outwards in the vicinity of the barrel wall, which then interacts with the surrounding hot fluid forming large vortical structures and bringing the cold fluid back to the vessel wall. The mixing of flow and penetration of colder temperatures in the downcomer is observed to be greatly influenced by interaction of these vortical structures. The descending cold plume in the downcomer is observed to form three branches separated by low-speed regions. The maximum values of turbulent kinetic energy are observed only in the vicinity of flow impingement, while high values of its production and dissipation are also observed within the shear layers of the descending plume. The maximum values of temperature fluctuations are found at the interface of the descending cold plume and surrounding hot fluid, while relatively high values are also seen at the locations of large vortical strucutres. Anisotropy in turbulence is also analysed using the componentality contour approach and a modified barycentric colour mapping scheme. Also reported herein is a comparison of mean and statistical profiles with those at lower Reynolds number reported in the literature. At higher Reynolds number, the cold impinging jet is deflected farther outwards in the downcomer. The locations of peak fluctuations in velocity and temperature are also farther away from the impingement. The magnitudes of fluctuating temperature and turbulent kinetic energy are observed to be higher for the present higher Reynolds number case. The peak Nusselt number at the barrel wall is observed to scale with a factor of Re1/2 in the present configuration.

An empirical study of the influences of gustiness on vertical mixing at the air-sea boundary

The exchange of momentum across the air-sea interface is a key driver of the earth system and its accurate parameterization is essential for precise weather and climate forecasting. However, our understanding of gustiness as an independent factor that can contribute to the momentum flux is limited. Using data collected from the R/P FLIP, as part of the Couple Air-Sea Processes and Electromagnetic ducting Research (CASPER) experiment, we explored the mechanisms by which gustiness contributes to the total interfacial momentum flux. We investigate how gustiness affects both the temporal and spatial (vertical) variance of turbulence in the atmospheric surface layer and show that high gustiness was associated with strong anisotropic turbulence at each measurement height. This was found to increase vertical wind fluctuations and inject additional momentum across the air-sea interface at lower wind speeds. Increased gustiness was also associated with the breakdown of the constant flux layer, which is generally assumed to exist over the ocean. This study has implications for both momentum flux parameterization and the use of similarity theory to model the flux-gradient relationship in the gusty atmospheric surface layer, thereby influencing the forecasting of climate and weather.

The Spiral Spectrum of a Laguerre–Gaussian Beam Carrying the Cross-Phase Propagating in Weak-to-Strong Atmospheric Turbulence

In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of utmost importance in the field of optical communications. However, most of the existing studies are limited to weak turbulence calculation models. In this paper, based on the extended Huygens–Fresnel integral, the analytical expression is derived for the mutual coherence function of a Laguerre–Gaussian beam carrying the cross-phase and propagating through weak-to-strong anisotropic Kolmogorov atmospheric turbulence; subsequently, the analytical expression is used to study the behavior of the spiral spectrum. The discrepancies in the spiral spectrum between weak and strong turbulence are comparatively studied. The influences of the cross-phase and the anisotropy of turbulence on the spiral spectrum are investigated through numerical examples. Our results reveal that the cross-phase determines the distribution of the spiral spectrum. The spiral spectrum can be tuned to multiple OAM modes through the adaptation of the cross-phase coefficient. Moreover, increasing the cross-phase coefficient can reduce both the discrepancies of the spiral spectrum under two computational methods and the effects of the anisotropic factors of turbulence on the spiral spectrum.

Propagation properties of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam through anisotropic atmospheric turbulence.

Using the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric turbulence has been theoretically derived. Detailed studies have been conducted on the evolution characteristics of the average intensity, the degree of coherence (DOC), and the degree of polarization (DOP) of the beam in turbulence. The results show that during propagation, the intensity distribution of the beam will exhibit a spiral structure, and the overall distribution of the light spots will rotate in a direction related to the sign of the topological charge. The DOC distribution of PCEShVB will display a pattern reminiscent of beam interference fringes with an increase in propagation distance, with the number of "interference fringes" greatly impacted by the hyperbolic sine parameter. Furthermore, PCEShVB with a large initial coherent length and hyperbolic sine parameter will increase the degree of separation of the spots and yield a large DOP. Finally, for the validation of the theoretical findings, the random phase screen method was employed to simulate the propagation of PCEShVB through anisotropic atmospheric turbulence. The studies revealed a consistent alignment between the simulation results and the theoretical predictions.

Energetic Stratified Turbulence Generated by Kuroshio–Seamount Interactions in Tokara Strait

Abstract Generating mechanisms and parameterizations for enhanced turbulence in the wake of a seamount in the path of the Kuroshio are investigated. Full-depth profiles of finescale temperature, salinity, horizontal velocity, and microscale thermal-variance dissipation rate up- and downstream of the ∼10-km-wide seamount were measured with EM-APEX profiling floats and ADCP moorings. Energetic turbulent kinetic energy dissipation rates and diapycnal diffusivities above the seamount flanks extend at least 20 km downstream. This extended turbulent wake length is inconsistent with isotropic turbulence, which is expected to decay in less than 100 m based on turbulence decay time of N−1 ∼ 100 s and the 0.5 m s−1 Kuroshio flow speed. Thus, the turbulent wake must be maintained by continuous replenishment which might arise from (i) nonlinear instability of a marginally unstable vortex wake, (ii) anisotropic stratified turbulence with expected downstream decay scales of 10–100 km, and/or (iii) lee-wave critical-layer trapping at the base of the Kuroshio. Three turbulence parameterizations operating on different scales, (i) finescale, (ii) large-eddy, and (iii) reduced-shear, are tested. Average ε vertical profiles are well reproduced by all three parameterizations. Vertical wavenumber spectra for shear and strain are saturated over 10–100 m vertical wavelengths comparable to water depth with spectral levels independent of ε and spectral slopes of −1, indicating that the wake flows are strongly nonlinear. In contrast, vertical divergence spectral levels increase with ε.

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

In situ observations of turbulence spectra in space plasmas are usually interpreted as wavenumber spectra, assuming that the fluctuation frequency is negligible in the plasma flow frame. We explore the effects of nonzero frequency in the plasma flow frame on turbulence spectral observations. The finite frequency can be caused by either propagating waves or nonlinear broadening of nonpropagating structures. We show that the observed frequency spectrum can be modified by the nonzero frequency of turbulent fluctuations in several ways. Specifically, (i) frequency broadening results in a minor modification to the observed spectrum, primarily acting as a smoothing kernel of the spectrum near the spectral break, while the asymptotic spectral index remains unchanged; (ii) wave propagation can affect the observed spectral index for anisotropic turbulence. The effect is significant at low frequencies and weaker at high frequencies, leading to a “concave” shape of the observed perpendicular spectrum; (iii) the Doppler shift for forward- and backward-propagating Elsasser modes can result in a nonzero cross helicity for critical-balanced turbulence since the effect of the Doppler shift favors outward-propagating waves systematically, resulting in an observed imbalance. These results may have important implications for the interpretation of solar wind flows observed by Parker Solar Probe.

Turbulence anisotropy effects on corner-flow separation: physics and turbulence modelling

The secondary motion caused by turbulence anisotropy is one of the crucial factors for determining the size of corner-flow separation in a side-wall interference flow field. Therefore, through a wall-resolved large-eddy simulation (LES) of a side-wall interference flow field, this study investigates the effects of the secondary motion on the corner-flow separation and explores the turbulence modelling that can reproduce the secondary flow motion. The momentum transport analysis using the LES results shows that the secondary vortex has twofold effects on delaying the corner-flow separation: the convective transport of the streamwise momentum towards the corner, and the enhanced production of turbulence by increasing the shear. Also, the vorticity transport analysis reconfirms that the secondary motion is caused primarily by turbulence anisotropy in the outer layer of the turbulent boundary layer. Furthermore, a quadratic constitutive relation (QCR) is proposed based on the analysis of the relationship between the Reynolds stress and velocity gradient. The proposed QCR consists of two quadratic terms and three constant parameters. The a priori analysis using the LES data shows that the proposed QCR represents the anisotropy of the Reynolds stress overall better than the existing QCR. Reynolds-averaged Navier–Stokes simulation using the proposed QCR with the Spalart–Allmaras turbulence model shows improvements in the prediction of the corner-flow separation compared to the results obtained by the existing QCR with the same turbulence model.

Exploring intermittency in numerical simulations of turbulence using single and multi-spacecraft analysis

The energy dissipation in collisionless plasmas as the solar wind is not yet fully understood. The intermittent nature of magnetic structures appears to be a fundamental part of the energy cascade. Understanding energy transfer and dissipation in the solar wind requires an accurate description of its intermittency. Upcoming multi-spacecraft missions will provide new insight on this matter. However, the use of multi-point data requires developing new data analysis techniques as well as cross-validating these techniques. In this study, we address the latter and explore the intermittency in a 3D simulation of anisotropic plasma turbulence using two approaches. We implement the standard single-spacecraft partial variance increments technique as well as a multi-point partial variance increments technique. We contrast these two techniques and explore their dependence on the angle between the spacecraft-configuration travel direction and the background magnetic field.

Numerical study of anisotropic turbulence in entrance-blocked narrow rectangular channel

Numerical study of turbulent flow in a narrow rectangular channel with side entrance blockage ratio from 0.25 to 0.9 was conducted under Reynolds numbers (Re) from 2,180 to 100,900. The Pearson similarity criterion was evaluated for mesh size sensitivity and turbulent models based on experimental data. Based on the validated turbulent model, predicted turbulent flow was studied.The entrance blocked channel forms jet-flow at inlet, shear-flow layer and recirculation vortex downstream of the blockage, with high Reynolds stress in the shear-flow layer. Then the streamwise flow reattaches the side channel wall. With blockage ratio increasing, the time-averaged velocity and Reynolds stress increase. With Re increasing, the time-averaged velocity and Reynolds stress decrease. The reattachment length increases in exponential law with blockage ratio and in power function with Re.The strong anisotropic turbulent flow in entrance-blocked narrow rectangular channel was evaluated by the Lumley triangle. In the streamwise plane, the anisotropic states in the recirculation vortex spread in the Lumley triangle, and they are two-dimensional wall turbulence in shear-flow layer and streamwise flow. Generally, the anisotropic states are dominated by two-dimensional wall turbulence and show tendency toward isotropic turbulence with Re increasing. The anisotropic states become towards isotropic in the recirculation vortex, stable in two-dimensional wall turbulence in shear-flow layer and one-dimensional turbulence in streamwise flow with blockage ratio increasing. These findings improve understandings of turbulent flow in the entrance blocked narrow channel.

On local isotropy and scale dependence of pair dispersion in turbulent canopy flows

Canopy flows in the atmospheric surface layer play important economic and ecological roles, governing the dispersion of passive scalars in the environment. The interaction of high-velocity fluid and large-scale surface-mounted obstacles in canopy flows produces drag and causes intense, inhomogeneous and anisotropic turbulence. In this work, we focus on the turbulent dispersion of passive scalars by studying the ‘pair dispersion’ – a statistical measure of relative motion between particles. We analyse the results of a three-dimensional particle tracking velocimetry experiment in a wind-tunnel canopy flow, focusing on small scales. We confirm the existence of local isotropy of pair dispersion at scales smaller than a characteristic shear length scale $L_\varGamma =(\epsilon /\varGamma ^3)^{1/2}$ , where $\epsilon$ and $\varGamma$ are the mean dissipation rate and shear rate, respectively. Furthermore, we show that pair dispersion in this locally isotropic regime is a scale-dependent super-diffusive process, similar to what occurs in homogeneous isotropic turbulent flows. In addition, we measure the pair relative velocity correlation function, showing that its de-correlation occurs in the locally isotropic regime, and discuss the implications of this observation for modelling pair dispersion. Thus, our study extends the fundamental understanding of turbulent pair dispersion to the anisotropic inhomogeneous turbulent canopy flow, bringing valuable information for modelling scalar dispersion in the atmospheric surface layer.

Improved prediction of turbomachinery flows using Reynolds stress model with [formula omitted] transition model

Transition is a prominent flow phenomenon in turbomachinery, especially at low and moderate Reynolds numbers. The turbomachinery internal flow often encounters complex vortex structures, typically accompanied by strong turbulence anisotropy and non–equilibrium. Conventional Reynolds–averaged Navier–Stokes (RANS) modeling with linear eddy–viscosity models (LEVMs) may fail short in capturing certain complex flow features. The Reynolds stress model (RSM) based on a higher turbulence closure level has more potential to reasonably consider turbulence anisotropy and non–equilibrium for such complex flows within turbomachinery than the LEVMs. However, the current RSM lacks an effective representation of transition phenomena. This paper presents an improved prediction of turbomachinery flows using RSM with transition modeling. The transition effects are incorporated into the RSM (SSG/LRR–ω model) via Menter's γ transport equation. The blending of the SSG/LRR–ω model with the γ transition model (SSG/LRR–ω–γ model) is firstly validated based on the T3 series flat plate cases with zero pressure gradient (T3A, T3B, T3A–) and variable pressure gradients (T3C1–C5). Comparisons with experiments show that the SSG/LRR–ω–γ model predicts corner separation flows with transition more accurately, although there is still room for further improvement. Then, the performance of the SSG/LRR–ω–γ model is assessed in a linear highly loaded prescribed velocity distribution (PVD) cascade and a NACA65 K48 compressor cascade. Comparisons with experiments indicate that, in both compressor cascades, the SSG/LRR–ω–γ model can predict more accurately corner flows with boundary layer transition on suction surfaces than the SSG/LRR–ω and SST model. Nevertheless, it still exhibits a tendency to overestimate the size of corner separation, especially in cases characterized by strong adverse pressure gradients. Comparisons of skin friction and velocity profiles predicted by the SSG/LRR–ω model with and without transition modeling illustrate the rationale behind the improved prediction. Further improvement of the SSG/LRR–ω–γ model for predicting turbomachinery corner flows should be conducted in future.

Time-mean equation and multi-field coupling numerical method for low-Reynolds-number turbulent flow in ferrofluid

Significant breakthroughs in the theory and applications of ferrofluid have broadened their usage in areas such as sealing and actuation. However, the development of numerical ferrofluid dynamics has been slow owing to inadequate multi-field coupling techniques and incomplete equations for turbulence in ferrofluid flow. The understanding of low-Reynolds-number turbulent flow mechanisms in ferrofluid at small scales, particularly in sealing and actuation applications, remains limited, therefore hindering further advancements. This article delves into the turbulent flow equations for general fluid and discusses the influence of different-scale vortices on the average fluid motion. An anisotropic turbulence model was introduced and verified using fluid flow around a cylinder. Magnetic and flow fields data were coupled through node ranking and interpolation methods. By introducing the interaction force of magnetic dipoles, the turbulent equations were refined within Euler grids, thereby establishing a numerical model for the turbulent motion of ferrofluids influenced by multiple fields. This model was applied to study the deformation and migration processes of ferrofluid under an external magnetic field. The variations in ferrofluid motion under magnetic forces were encapsulated, and macroscopic flow comparisons were made through experiments, which demonstrated good consistency. This research provides new methods and ideas for use in ferrofluid numerical studies. Additionally, it offers valuable technical support that can aid in developing industrial products such as sealing and driving devices based on ferrofluids.

Deformation and Breakup of Bubbles and Drops in Turbulence

Fragmentation of bubbles and droplets in turbulence produces a dispersed phase spanning a broad range of scales, encompassing everything from droplets in nanoemulsions to centimeter-sized bubbles entrained in breaking waves. Along with deformation, fragmentation plays a crucial role in enhancing interfacial area, with far-reaching implications across various industries, including food, pharmaceuticals, and ocean engineering. However, understanding and modeling these processes are challenging due to the complexity of anisotropic and inhomogeneous turbulence typically involved, the unknown residence time in regions with different turbulence intensities, and difficulties arising from the density and viscosity ratios. Despite these challenges, recent advances have provided new insights into the underlying physics of deformation and fragmentation in turbulence. This review summarizes existing works in various fields, highlighting key results and uncertainties, and examining the impact on turbulence modulation, drag reduction, and heat and mass transfer.