## What is/are Isotropic Turbulence?

Isotropic Turbulence - Rms turbulent velocities, u ' , created by four peripheral variable speed fans, were measured by Particle Image Velocimetry, PIV, which indicated near-uniform, isotropic turbulence, with small mean velocities.^{[1]}Here, we describe an experimental study on the dynamics of thin cylindrical shells resembling broken bottle fragments settling through quiescent fluid and homogeneous anisotropic turbulence.

^{[2]}This study presents the effects of the conservation error of turbulent kinetic energy on the isotropic turbulence field.

^{[3]}These features can be successfully predicted by modern models that take into account the specifics of flows with heterogeneous anisotropic turbulence.

^{[4]}The simulation was conducted within a constant volume with an isotropic turbulence condition under 40 bar.

^{[5]}In this work, we analyze the capacity of the superstatistics construction to provide modeling of the velocity field probability density functions (PDFs) of isotropic turbulence.

^{[6]}We present a quantitative analysis of the inertial range statistics produced by entropic lattice Boltzmann method (ELBM) in the context of three-dimensional homogeneous and isotropic turbulence.

^{[7]}These flow mechanisms comprise a shear layer near the interface, lateral momentum transfer and strong secondary currents due to the non-isotropic turbulence.

^{[8]}We study turbulent properties of the ISM to show that, in the case where the break scale traces a transition to isotropic turbulence, the fraction of required accretion energy to sustain turbulent motions in the ISM increases significantly.

^{[9]}This noise prediction model relies on the accuracy of the turbulence spectrum, which is usually assumed to be the von Kármán energy spectrum for isotropic turbulence.

^{[10]}Anisotropic turbulence of the Reynolds Stress Model (RSM) is used in modeling turbulent fluid (natural gas) and.

^{[11]}This indicates that the lower PMSE layers are associated with more anisotropic turbulence scattering.

^{[12]}The proposed power spectrum can handle general non-Kolmogorov, anisotropic turbulence but reduces to Kolmogorov, isotropic case if the power law exponents of temperature and salinity are set to 11/3 and anisotropy coefficient is set to unity.

^{[13]}Based on the data analyses, anisotropic turbulence was observed in the cascade.

^{[14]}In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.

^{[15]}Numerical simulations of forced anisotropic turbulence (FAT) in a periodic box and homogeneous shear turbulence (HST) at various turbulent Mach (Ma${}_{\mathrm{T}}$) and Taylor Reynolds numbers are performed to study the anisotropy of kinetic energy (KE) transfer in compressible homogeneous turbulence.

^{[16]}It is shown that vertical velocity in clouds indeed can be represented as a sum of convective velocity (forming zone of cloud updrafts and subsiding shell) and a stochastic velocity obeying laws of homogeneous and isotropic turbulence.

^{[17]}The overall approach represents a combination of wall-blocking (non-local) and wall-viscous (low-Reynolds number) effects encountered in anisotropic turbulence.

^{[18]}For isotropic turbulence, in which l ∥ = l ∧ , Sonsrettee et al.

^{[19]}In these works, it is also shown that the developed two-fluid model is able to adequately describe complex anisotropic turbulences.

^{[20]}This experiment is used to study the origin of statistical irreversibility and the prevalence of direct over inverse energy cascades in isotropic turbulence.

^{[21]}Also, we find that the turbine generates its own kind of turbulence that dominates the ambient turbulence and has strong features of homogeneous, isotropic turbulence.

^{[22]}Using the mesh-free finite mass method as an example, we show that the anisotropic model is best able to reproduce the proper Kolmogorov inertial range scaling in homogeneous, isotropic turbulence.

^{[23]}These results were found in both isotropic and anisotropic turbulence fields.

^{[24]}Temporal evolution of the scaling exponent from Fourier power analysis suggests slightly below the classical Kolmogorov value of −5/3 for the three-dimensional homogeneous and isotropic turbulence.

^{[25]}Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence.

^{[26]}One direction of research is to investigate anisotropic turbulence intensities, id est to investigate the distribution of Reynolds stresses and energy spectra in a square cross-section channel, downstream of a semi-active jet turbulence grid generating anisotropic turbulent airflow.

^{[27]}Further, to understand the deviation from the isotropic turbulence, the turbulence triangle, Eigen values, and the invariant functions are presented at the downstream of the grid for the three oscillating flow cases.

^{[28]}We propose a new theory of pair diffusion in homogeneous, isotropic turbulence hypothesizing that not only structures of size l, but much larger ones also induce significant pair separation—ignored in the R-O theory.

^{[29]}Droplet evaporation and combustion in isotropic turbulence were considered.

^{[30]}We test the utility of these particles by measuring their dissolution rates in homogeneous, isotropic turbulence in our laboratory turbulence tank.

^{[31]}We present a method to identify such manifolds, and we apply it to a reduced model for the Lagrangian evolution of field gradients in homogeneous and isotropic turbulence with a passive scalar.

^{[32]}Standard models are often not sufficient to accurately predict vortices, which can have a huge impact on the performance, since based on the assumption of isotropic turbulence.

^{[33]}, laminar burning velocity, turbulent burning velocity) of diethyl ether (DEE)/air mixtures under different pre-ignition quasi-isotropic turbulence velocity.

^{[34]}The results show the estimation of the deviation measure from the isotropic turbulence in view of Reynolds stress tensor for turbulent flow in the presence of seepage through the channel bed.

^{[35]}An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

^{[36]}This work is aimed at establishing a theoretical method for predicting confined methane-air explosion pressure under isotropic turbulence.

^{[37]}We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in three-dimensional, homogeneous and isotropic turbulence.

^{[38]}Comparison is made with homogeneous-isotropic turbulence, in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend.

^{[39]}The present work also demonstrates that the use of anisotropic turbulence models, which may become more common in the future due to the evolution of engine architectures, must be done carefully because of the sensitivity of the models to the anisotropic parameters which are difficult to assess from RANS simulations.

^{[40]}The turbulent wave activity (slope in the power spectrum) reduces with a decrease in gas shear, and shows similarities to the decay of homogeneous and isotropic turbulence.

^{[41]}It is found that in isotropic turbulence fractional derivative order $\alpha \sim 0.

^{[42]}These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation.

^{[43]}Linear two equation models are often not able to represent these effects correctly since their derivation is based on over-simplifications, such as the Boussinesq hypothesis, which makes it impossible to capture anisotropic turbulence.

^{[44]}A three-dimensional remeshed smoothed particle hydrodynamics method for the simulation of isotropic turbulence is used, the method is coupled with Brinkman penalisation technique for flow simulation inside the complex valve geometry.

^{[45]}A framework is proposed to investigate the behavior of LES flame surface density models for simple academic cases, here the development of a statistically one-dimensional flame in an homogenous and isotropic turbulence, by comparison with a prescribed reference solution.

^{[46]}This study presents the effects of spatial resolution anisotropy on an isotropic turbulence field.

^{[47]}These polynomials, denoted by Sn(x) and called special polynomials, were first discovered in a study of a certain family of isotropic turbulence fields.

^{[48]}An experimental investigation of the time-dependent spatial distribution of droplet concentration in a “box” of stationary homogeneous and isotropic turbulence without mean flow was performed for polydispersed droplet clouds with a wide range of mean droplet diameters and droplet size distributions, characterized by a representative Stokes number, based on the droplet arithmetic diameter and the Kolmogorov time scale of the flow, varying between 0.

^{[49]}62 at 298 K, using the same dual-chamber, fan-stirred cruciform burner capable of generating near-isotropic turbulence.

^{[50]}

## direct numerical simulation

The SGS model presented here is verified using direct numerical simulation (DNS) data for particle-laden homogenous isotropic turbulence.^{[1]}Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds number R_{λ}∼1000.

^{[2]}Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.

^{[3]}We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data.

^{[4]}Direct numerical simulations (DNS) of the evaporation of interface-resolved n-heptane fuel droplets in forced homogeneous isotropic turbulence (HIT) are performed at 10 bar and 348 K.

^{[5]}In this work, we investigate the intrinsic nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in homogeneous isotropic turbulence (HIT).

^{[6]}The dynamics of intense vorticity is investigated by means of synchronisation experiments in direct numerical simulations of isotropic turbulence.

^{[7]}We study bubble break-up in homogeneous and isotropic turbulence by direct numerical simulations of the two-phase incompressible Navier–Stokes equations.

^{[8]}After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes.

^{[9]}The direct numerical simulation results of three academic configurations (homogeneous isotropic turbulence, mixing layer, and channel flow) are filtered from the largest scale in the domain down to the Kolmogorov length scale.

^{[10]}Our model is validated using three examples: (i) recovering the original flow field from filtered data using direct numerical simulation (DNS) of homogeneous isotropic turbulence; (ii) reconstructing full-resolution fields using partially measured data from the DNS of turbulent channel flows; and (iii) generating a DNS-resolution flow field from large-eddy simulation (LES) data for turbulent channel flows.

^{[11]}The theoretical prediction is verified by direct numerical simulations of mass transfer of dilute gas from a bubble in homogeneous and isotropic turbulence, and very good agreement is observed as long as the thin boundary layer is properly resolved.

^{[12]}Finally, we demonstrate the error bound numerically using synthetic three-dimensional data sets based on direct numerical simulations of homogeneous isotropic turbulence and transitional boundary layer flow provided by Johns Hopkins University (Li et al.

^{[13]}In this paper, we study polymer scission in homogeneous isotropic turbulence, through a combination of stochastic modelling, based on a Gaussian time-decorrelated random flow, and direct numerical simulations (DNS) with both one-way (passive) and two-way (active) coupling of the polymers, modelled as bead-spring chains, and the flow.

^{[14]}Direct numerical simulation (DNS) of initially non-premixed fuel–air mixtures developing in forced isotropic turbulence have been carried out to investigate the proposed model.

^{[15]}We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence and investigate the dynamics of different particle shapes at different scales in turbulence using a filtering approach.

^{[16]}The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations.

^{[17]}These quantities are analyzed by considering direct numerical simulation databases of premixed flame kernel growth in homogeneous isotropic turbulence.

^{[18]}By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$.

^{[19]}We study the correlation function and mean linear response function of the velocity Fourier mode of statistically steady-state, homogeneous and isotropic turbulence in Eulerian and Lagrangian coordinates through direct numerical simulation (DNS).

^{[20]}In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme.

^{[21]}Path instability of a millimetric spheroidal bubble in isotropic turbulence is investigated by direct numerical simulation combined with an immersed boundary method.

^{[22]}Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9.

^{[23]}In this work, a skeletal n-heptane chemical mechanism including low-temperature chemistry is used to conduct two-dimensional Direct Numerical Simulations (DNS) of nonpremixed “cool” flames subjected to unsteady, two-dimensional flow initialized from a plane of isotropic turbulence.

^{[24]}In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime.

^{[25]}The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations.

^{[26]}The effect of free-slip and no-slip boundaries on isotropic turbulence is studied by direct numerical simulation (DNS).

^{[27]}Direct numerical simulations of an aggregation system composed of monosized spherical particles in homogeneous isotropic turbulence have been performed using Lattice Boltzmann method (LBM).

^{[28]}The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor is decomposed into three components representing an irrotational straining motion.

^{[29]}We study the Reynolds number scaling of the Kolmogorov-Sinai entropy and attractor dimension for three-dimensional homogeneous isotropic turbulence through the use of direct numerical simulation.

^{[30]}Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence.

^{[31]}This study is based on a series of direct numerical simulations of homogeneous and isotropic turbulence in the presence of an initially flat interface that separates two fluids of equal densities and viscosities.

^{[32]}A priori analysis using direct numerical simulation (DNS) data for scalar mixing in homogeneous isotropic turbulence is also performed.

^{[33]}Lastly, we apply the new wavelet-decomposition tools in analysing the direct numerical simulation data of droplet-laden decaying isotropic turbulence (in absence of gravity) of Dodd & Ferrante ( J.

^{[34]}

## turbulent channel flow

This hybrid RANS/LES model code was successfully validated by simulation of homogeneous isotropic turbulence, turbulent channel flow, and backward facing step flow.^{[1]}3 The performance of this special configuration has been successfully tested for decaying isotropic turbulence and a turbulent channel flow.

^{[2]}The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

^{[3]}We show that the modified initialization greatly improves tracking in two canonical cases, homogeneous isotropic turbulence and turbulent channel flow (inhomogenous and anisotropic), greatly increasing the percentage of correct tracks found even under challenging seeding/particle displacement conditions.

^{[4]}

## large eddy simulation

We propose a model for large-eddy simulation (LES) of decaying isotropic turbulence laden with droplets with diameter of Taylor length-scale.^{[1]}[“Large-eddy simulations of forced isotropic turbulence with viscoelastic fluids described by the finitely extensible nonlinear elastic rheological model with Peterlin's closure model,” Phys.

^{[2]}We demonstrate the potential of this approach on large-eddy simulations of isotropic turbulence, using the recovery of statistical properties of direct numerical simulations as a reward.

^{[3]}The results of the large eddy simulation are used to further analyze the distribution of the validity parameter ρ RS and the anisotropic turbulence field.

^{[4]}

## order velocity structure

A model for the third-order velocity structure function, S3, is proposed for closing the transport equation of the second-order velocity structure function, S2, in the scaling range of finite Reynolds number homogeneous and isotropic turbulence (HIT).^{[1]}Numerical calculations based on a recent version of the eddy-damped quasi-normal model (EDQNM-LMFA) are carried out for homogeneous isotropic turbulence (HIT) with the aim of investigating the dependency on the Reynolds number of second and third order velocity structure functions.

^{[2]}

## turbulent boundary layer

Finally, it is demonstrated that the observed first-order phenomena in a turbulent boundary layer subjected to FST can be modelled by superimposing an isotropic turbulence field on a turbulent boundary layer field, which supports the hypothesis that the underlying structure of the boundary layer appears to remain largely intact if the naturally occurring fluctuations in the turbulent boundary layer exceed the energy of the FST.^{[1]}

## Homogeneou Isotropic Turbulence

Focusing on physical space forcing, these methods are usually first evaluated upon sustained homogeneous isotropic turbulence by introducing a body force to the Navier–Stokes equations.^{[1]}A new kind of turbulence tunnel, the pure coherent shear source turbulence tunnel, proposed to produce high Reynolds number, approximately homogeneous isotropic turbulence is studied computationally.

^{[2]}Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finitevolume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate.

^{[3]}These two weaknesses separate AEH from more credible theories like Kolmogorov's theory of homogeneous isotropic turbulence, which, despite its phenomenological nature, has one velocity scaling, i.

^{[4]}The increase in the spectral width of an initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated by applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or a Lagrangian particle-based scheme.

^{[5]}Soniс boom propagation in the atmospheric turbulent layer, represented by a model of homogeneous isotropic turbulence, is investigated numerically in two-dimensional geometry using a KZK-type nonlinear parabolic equation for an inhomogeneous moving medium with relaxation.

^{[6]}These methods are then used to study differential diffusion of scalars on two canonical cases: Homogeneous Isotropic Turbulence and a jet flow.

^{[7]}A two-dimensional decaying homogeneous isotropic turbulence is considered for the demonstration of AE.

^{[8]}This hybrid RANS/LES model code was successfully validated by simulation of homogeneous isotropic turbulence, turbulent channel flow, and backward facing step flow.

^{[9]}Direct numerical simulations (DNS) of the evaporation of interface-resolved n-heptane fuel droplets in forced homogeneous isotropic turbulence (HIT) are performed at 10 bar and 348 K.

^{[10]}Self-propagation of a reaction wave, which consists of an infinitely thin reaction zone (front) and a thick inert mixing layer adjacent to the front, in constant-density statistically stationary, homogeneous isotropic turbulence unaffected by the wave is analytically studied.

^{[11]}In this work, we investigate the intrinsic nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in homogeneous isotropic turbulence (HIT).

^{[12]}Solid particles with diameters smaller than the Kolmogorov length scale ($d_p<\eta$) are initially aggregated into a spherical ‘clump’ of diameter $D>\eta$ and placed in homogeneous isotropic turbulence.

^{[13]}The results prove that the present vessel can be conveniently adopted for several turbulent combustion studies including mainly the determination of turbulent burning velocity for gaseous premixed flames in nearly homogeneous isotropic turbulence.

^{[14]}A single-time two-point spectral closure is developed by approximation of the Lagrangian direct interaction approximation (LDIA) for a passive scalar in the presence of a mean scalar gradient in homogeneous isotropic turbulence.

^{[15]}Reduced models describing the Lagrangian dynamics of the Velocity Gradient Tensor (VGT) in Homogeneous Isotropic Turbulence (HIT) are developed under the Physics-Informed Machine Learning (PIML) framework.

^{[16]}The analysis shows an agreement in comparison with previous results from homogeneous isotropic turbulence (HIT) using the multifractal model, extended self-similarity and velocity increments’ autocorrelations.

^{[17]}Here, sonic boom propagation through homogeneous isotropic turbulence is simulated using the KZK equation.

^{[18]}Periodic boxes of homogeneous isotropic turbulence are generated using the linear forcing method at R e λ = 29 , 51 , and 120.

^{[19]}We conduct numerical investigations on the early-stage agglomeration of identically charged microparticles in homogeneous isotropic turbulence.

^{[20]}After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes.

^{[21]}This work analyses the homogeneous isotropic turbulence by means of the equivalence between Euler and Lagrange representations of motion, adopting the bifurcation rates associated with Navier–Stokes and kinematic equations, and an appropriate hypothesis of fully developed chaos.

^{[22]}The direct numerical simulation results of three academic configurations (homogeneous isotropic turbulence, mixing layer, and channel flow) are filtered from the largest scale in the domain down to the Kolmogorov length scale.

^{[23]}We investigate the dynamics of inertial particles in homogeneous isotropic turbulence, under one-way momentum coupling, using a new computational approach that incorporates the effect of long-range many-body aerodynamic interactions along with the short-range lubrication forces.

^{[24]}The distortion of homogeneous isotropic turbulence interacting with a porous cylinder is calculated by means of the rapid distortion theory (RDT).

^{[25]}The behavior of the model is first analyzed on an a priori 1D-study and is consequently validated on a 3-D turbulent flame propagation in Homogeneous Isotropic Turbulence (HIT).

^{[26]}Our model is validated using three examples: (i) recovering the original flow field from filtered data using direct numerical simulation (DNS) of homogeneous isotropic turbulence; (ii) reconstructing full-resolution fields using partially measured data from the DNS of turbulent channel flows; and (iii) generating a DNS-resolution flow field from large-eddy simulation (LES) data for turbulent channel flows.

^{[27]}Further, we investigate how commutation error manifests in simulation and demonstrate its impact on the convection of a packet of homogeneous isotropic turbulence through an inhomogeneous grid.

^{[28]}We investigate the dynamics of cohesive particles in homogeneous isotropic turbulence, based on one-way coupled simulations that include Stokes drag, lubrication, cohesive and direct contact forces.

^{[29]}Its theoretical value assuming homogeneous isotropic turbulence is - 0.

^{[30]}In the limit of very large Reynolds numbers for homogeneous isotropic turbulence of an incompressible fluid, the statistics of the velocity differences between two points in space are expected to approach universal power laws at scales smaller than those at which energy is injected.

^{[31]}Finally, we demonstrate the error bound numerically using synthetic three-dimensional data sets based on direct numerical simulations of homogeneous isotropic turbulence and transitional boundary layer flow provided by Johns Hopkins University (Li et al.

^{[32]}In this paper, we study polymer scission in homogeneous isotropic turbulence, through a combination of stochastic modelling, based on a Gaussian time-decorrelated random flow, and direct numerical simulations (DNS) with both one-way (passive) and two-way (active) coupling of the polymers, modelled as bead-spring chains, and the flow.

^{[33]}This explains the observed preferential spinning of rods and tumbling of disks, similar to that in homogeneous isotropic turbulence, even at the early stage when the flow is anisotropic and laminar.

^{[34]}Finally, a 3D two-phase Homogeneous Isotropic Turbulence (HIT) configuration is presented to demonstrate the potential of this method in presence of breakup, gas encapsulation, coalescence and evaporation processes.

^{[35]}The non-dimensional prefactor of the Kolmogorov 2/3 law in the inertial range of homogeneous isotropic turbulence (HIT) has been believed to be a universal constant for many years, and then people.

^{[36]}The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

^{[37]}We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence and investigate the dynamics of different particle shapes at different scales in turbulence using a filtering approach.

^{[38]}Specifically, we measured the orientation and rotation rate of the fibres, and we can confirm that in the centre, the most homogeneous part of the channel, statistics, although influenced by the curvature, bear similarities to those obtained in previous investigations in homogeneous isotropic turbulence.

^{[39]}These quantities are analyzed by considering direct numerical simulation databases of premixed flame kernel growth in homogeneous isotropic turbulence.

^{[40]}Numerical calculations based on a recent version of the eddy-damped quasi-normal model (EDQNM-LMFA) are carried out for homogeneous isotropic turbulence (HIT) with the aim of investigating the dependency on the Reynolds number of second and third order velocity structure functions.

^{[41]}By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$.

^{[42]}The flames are propagating in a rectangular box under homogeneous isotropic turbulence conditions over a wide range of Karlovitz numbers.

^{[43]}The influence of statistically stationary, homogeneous isotropic turbulence (i) on the mean area of a passive front propagating in a constant-density fluid and, hence, (ii) on the mean fluid consumption velocity u¯T is explored, particularly in the case of an asymptotically high turbulent Reynolds number, and an asymptotically high ratio of the Kolmogorov velocity to a constant speed u0 of the front.

^{[44]}In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme.

^{[45]}Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions.

^{[46]}This Letter is focused on characterizing the effects of numerical dispersion error by studying the energy cascade in LES of convecting homogeneous isotropic turbulence.

^{[47]}Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9.

^{[48]}We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence.

^{[49]}We show that the modified initialization greatly improves tracking in two canonical cases, homogeneous isotropic turbulence and turbulent channel flow (inhomogenous and anisotropic), greatly increasing the percentage of correct tracks found even under challenging seeding/particle displacement conditions.

^{[50]}

## Decaying Isotropic Turbulence

The analytical development is performed, applying the Hybrid-Equivalence criterion, and the model is calibrated in decaying isotropic turbulence.^{[1]}We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data.

^{[2]}We apply this analysis to a two-dimensional decaying isotropic turbulence.

^{[3]}We propose a model for large-eddy simulation (LES) of decaying isotropic turbulence laden with droplets with diameter of Taylor length-scale.

^{[4]}The rate at which the ‘four-fifths’ law and ‘four-thirds’ law were approached by the third-order structure functions was found to be more gradual than decaying isotropic turbulence for the same Reynolds numbers.

^{[5]}Before focusing on the BFS flow, we investigated the impact of the AMD model coefficient magnitude on the numerical predictions of the decaying isotropic turbulence flow.

^{[6]}3 The performance of this special configuration has been successfully tested for decaying isotropic turbulence and a turbulent channel flow.

^{[7]}The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations.

^{[8]}The effect of the inter-grid correction is demonstrated by investigating advection of decaying isotropic turbulence across a coarse/fine and fine/coarse AMR grid interface.

^{[9]}Lastly, we apply the new wavelet-decomposition tools in analysing the direct numerical simulation data of droplet-laden decaying isotropic turbulence (in absence of gravity) of Dodd & Ferrante ( J.

^{[10]}

## Compressible Isotropic Turbulence

The transfer of internal energy fluctuation is numerically investigated for the stationary compressible isotropic turbulence in vibrational non-equilibrium with large-scale thermal forcing.^{[1]}Interscale kinetic energy transfer in chemically reacting compressible isotropic turbulence is studied using numerical simulations at turbulent Mach numbers 0.

^{[2]}The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations.

^{[3]}In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime.

^{[4]}

## Forced Isotropic Turbulence

Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.^{[1]}[“Large-eddy simulations of forced isotropic turbulence with viscoelastic fluids described by the finitely extensible nonlinear elastic rheological model with Peterlin's closure model,” Phys.

^{[2]}Direct numerical simulation (DNS) of initially non-premixed fuel–air mixtures developing in forced isotropic turbulence have been carried out to investigate the proposed model.

^{[3]}

## Steady Isotropic Turbulence

The Reynolds number dependence of steady isotropic turbulence is used to validate the present analysis.^{[1]}It is first shown that the energy cascade in statistically steady isotropic turbulence is local in scale, at least on average, and that temporal variations of the large-scale forcing are transferred to smaller scales as a ‘wave’ consistent with the classical Kolmogorov model.

^{[2]}

## Homogenou Isotropic Turbulence

The SGS model presented here is verified using direct numerical simulation (DNS) data for particle-laden homogenous isotropic turbulence.^{[1]}In this study, homogenous isotropic turbulence with Taylor's Reynolds number of 102.

^{[2]}

## Dimensional Isotropic Turbulence

We introduce a network (graph) theoretic community-based framework to extract vortical structures that serve the role of connectors for the vortical interactions in two- and three-dimensional isotropic turbulence.^{[1]}Recently, making use of a numerical model with three dimensional isotropic turbulence, the influence of turbulence intermittency and magnetic fluctuations on the energetic particle transport was investigated in the solar wind context.

^{[2]}

## isotropic turbulence field

This study presents the effects of the conservation error of turbulent kinetic energy on the isotropic turbulence field.^{[1]}These results were found in both isotropic and anisotropic turbulence fields.

^{[2]}Finally, it is demonstrated that the observed first-order phenomena in a turbulent boundary layer subjected to FST can be modelled by superimposing an isotropic turbulence field on a turbulent boundary layer field, which supports the hypothesis that the underlying structure of the boundary layer appears to remain largely intact if the naturally occurring fluctuations in the turbulent boundary layer exceed the energy of the FST.

^{[3]}The results of the large eddy simulation are used to further analyze the distribution of the validity parameter ρ RS and the anisotropic turbulence field.

^{[4]}This study presents the effects of spatial resolution anisotropy on an isotropic turbulence field.

^{[5]}These polynomials, denoted by Sn(x) and called special polynomials, were first discovered in a study of a certain family of isotropic turbulence fields.

^{[6]}

## isotropic turbulence laden

We propose a model for large-eddy simulation (LES) of decaying isotropic turbulence laden with droplets with diameter of Taylor length-scale.^{[1]}The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations.

^{[2]}

## isotropic turbulence model

The present work also demonstrates that the use of anisotropic turbulence models, which may become more common in the future due to the evolution of engine architectures, must be done carefully because of the sensitivity of the models to the anisotropic parameters which are difficult to assess from RANS simulations.^{[1]}We illustrate this method for a simple, isotropic turbulence model and we find remarkable agreement with the results of numerical studies.

^{[2]}

## isotropic turbulence reveal

Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finitevolume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate.^{[1]}Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.

^{[2]}

## isotropic turbulence condition

The simulation was conducted within a constant volume with an isotropic turbulence condition under 40 bar.^{[1]}The flames are propagating in a rectangular box under homogeneous isotropic turbulence conditions over a wide range of Karlovitz numbers.

^{[2]}