## What is/are Isotropic Turbulent?

Isotropic Turbulent - What makes this model different is that it can describe strongly anisotropic turbulent flows; moreover, it is easy to implement numerically while not being computationally expensive.^{[1]}We investigate the dynamics of turbulent dispersion by means of direct numerical simulations of a passive tracer released in a homogeneous isotropic turbulent flow.

^{[2]}The physical mechanisms underlying the dynamics of the flame kernel in stationary isotropic and anisotropic turbulent field are studied using large eddy simulations (LES) combined with a pdf approach method for the combustion model closure.

^{[3]}In this study, we investigate interscale kinetic energy transfer and subgrid-scale (SGS) backscatter using data from direct numerical simulations (DNSs) of premixed isotropic turbulent flames.

^{[4]}A distribution of Hill’s vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor.

^{[5]}A method for the numerical generation of anisotropic turbulent velocity fields is presented.

^{[6]}To enable an analysis uncomplicated by the presence of many coupled interactions, we confine our attention to the classic test case of monodisperse particles in homogeneous, isotropic turbulent flows, and subject to a uniform gravitational field.

^{[7]}Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered.

^{[8]}Generally, the theory correctly predicts the measured log-amplitude variances, which are affected primarily by small-scale, isotropic turbulent eddies.

^{[9]}Multi-wave band synchrotron linear polarization of gamma-ray burst (GRB) afterglows is studied under the assumption of an anisotropic turbulent magnetic field with a coherence length of the plasma skin-depth scale in the downstream of forward shocks.

^{[10]}On the base of Randomized Spectral Method (RSM), a new stochastic algorithm for the generation of homogeneous anisotropic turbulent velocity fields has been developed.

^{[11]}1 library, we study the flow of particles inside a highly anisotropic turbulent flow field of a hydrocyclone.

^{[12]}In this work, a numerical study of the dynamical behavior of unsteady and anisotropic turbulent flow downstream a 90° bended pipe was presented.

^{[13]}We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a stochastic vector field with a Gaussian distribution, and then a scalar advected by a homogeneous and isotropic turbulent flow described by the Navier-Stokes equation, under the assumption that the scalar is passive, i.

^{[14]}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.

^{[15]}The 3D PTV and particle identification algorithms show good consistencies under two types of flow conditions: a homogeneous isotropic turbulent flow and a vortex ring flow.

^{[16]}In this paper we study finite particle Reynolds number effects up to $Re_p=50$ on the dynamics of small spherical bubbles and solid particles in an isotropic turbulent flow.

^{[17]}In addition, the work also consists of implementing an appropriate turbulence model, to ensure a better analysis of free, homogeneous isotropic turbulent flows.

^{[18]}We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations.

^{[19]}The Reynolds stress data showed an anisotropic turbulent flow immediately downstream of the roller toe, and tended towards isotropy away from the roller toe.

^{[20]}Herein, we investigate the topology of the local flow in vaporizing forced homogeneous isotropic turbulent two-phase flows.

^{[21]}We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow.

^{[22]}Many flow configurations in nature and in the laboratories deviate from the ideal homogeneous and isotropic turbulent cases (HIT) characterised by the presence of direct energy cascade only and strong small-scales universality.

^{[23]}In this strongly anisotropic situation, despite the additional roughness induced by the canopy, it is shown that fluctuations of Lagrangian velocity increments over small time scales display very similar behaviour as those observed in homogeneous and isotropic turbulent flows.

^{[24]}Vortices motion in the anisotropic turbulent flow of cyclones makes a vital impact on flow stability and collection performance.

^{[25]}The covariance structure of a homogeneous isotropic turbulent wind velocity field is derived in terms of modified Bessel functions for an extended form of the Kàrmàn velocity spectrum, including explicit expressions for the transverse coherence functions.

^{[26]}Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered.

^{[27]}The method is demonstrated for a canonical Burgers vortex, a Bodewadt vortex, homogeneous isotropic turbulent flow, the wake of a propeller, a heaving plate, a turning containership and the airwake of a surface combatant.

^{[28]}A stochastic method basing on turbulence statistics is proposed to generate anisotropic turbulent fluctuations and track particles motion separately.

^{[29]}The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated.

^{[30]}We also show that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with kinetic Alfven wave-like fluctuations from the anisotropic turbulent cascade.

^{[31]}Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively.

^{[32]}Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum.

^{[33]}In this study, an anisotropic turbulent mixing model with a turbulent mixing coefficient matrix is developed and embedded in an in-house code to analyze the thermal-hydraulic performance of the fuel assembly.

^{[34]}Validation of the GRM method is carried out by generating and simulating a decaying homogeneous isotropic turbulent flow.

^{[35]}The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components.

^{[36]}The alignment between strain and mixture fraction gradient differs slightly from the homogeneous isotropic turbulent case but agree remarkably well with previous results observed in homogeneous shear incompressible flows.

^{[37]}In the wall-normal direction, particle distributions (mean/preferential concentration) exhibit two distinct behaviours in the inner flow and outer flow, corresponding to two highly anisotropic turbulent structures, LSMs and VLSMs.

^{[38]}This review devoted to the theoretical analysis, calculation, and modeling of the processes of merging and breakage of droplets and bubbles in an isotropic turbulent flow.

^{[39]}This Rapid Communication presents an advanced method to model isotropic turbulent inflow conditions for a two-dimensional vortex particle method.

^{[40]}A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero.

^{[41]}We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D).

^{[42]}EnglishBy using an active grid and a passive grid, a homogenous and isotropic turbulent flow was characterized by studying its longitudinal structure functions and transverse 〉 and where u is the longitudinal velocity fluctuation, and v is the fluctuation of the transverse velocity, as a function of the Reynolds number for orders, n, between 2 and 8.

^{[43]}By the spectrum average coherence length and the spectrum average mutual coherence function, we construct a received probability of vortex modes carried by localized wave of Bessel–Gaussian amplitude envelope in anisotropic turbulent seawater.

^{[44]}The mixing layer growth rate and the mixing efficiency both show reduction by increasing the initial magnetic field intensity, which is attributed to the reduction of the averaged Reynolds number of both homogenous isotropic turbulent regions due to the suppressing effect of the Lorentz force on the velocity fields of these regions.

^{[45]}We propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and fluid inertia forces in a homogeneous and isotropic turbulent flow.

^{[46]}We also find that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with fluctuations from the anisotropic turbulent cascade.

^{[47]}A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero.

^{[48]}Homogeneous and isotropic turbulent fields obtained from two DNS databases (with $\mbox{Re}_\lambda$ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories.

^{[49]}ABSTRACT In this paper, we study the correlation functions for magnetic energy and magnetic helicity generated by a small-scale dynamo mechanism in a mirror-asymmetric and isotropic turbulent conductive fluid.

^{[50]}

## Homogeneou Isotropic Turbulent

We investigate the dynamics of turbulent dispersion by means of direct numerical simulations of a passive tracer released in a homogeneous isotropic turbulent flow.^{[1]}The 3D PTV and particle identification algorithms show good consistencies under two types of flow conditions: a homogeneous isotropic turbulent flow and a vortex ring flow.

^{[2]}In addition, the work also consists of implementing an appropriate turbulence model, to ensure a better analysis of free, homogeneous isotropic turbulent flows.

^{[3]}We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations.

^{[4]}Herein, we investigate the topology of the local flow in vaporizing forced homogeneous isotropic turbulent two-phase flows.

^{[5]}The covariance structure of a homogeneous isotropic turbulent wind velocity field is derived in terms of modified Bessel functions for an extended form of the Kàrmàn velocity spectrum, including explicit expressions for the transverse coherence functions.

^{[6]}Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered.

^{[7]}The method is demonstrated for a canonical Burgers vortex, a Bodewadt vortex, homogeneous isotropic turbulent flow, the wake of a propeller, a heaving plate, a turning containership and the airwake of a surface combatant.

^{[8]}The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated.

^{[9]}Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively.

^{[10]}Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum.

^{[11]}Validation of the GRM method is carried out by generating and simulating a decaying homogeneous isotropic turbulent flow.

^{[12]}The alignment between strain and mixture fraction gradient differs slightly from the homogeneous isotropic turbulent case but agree remarkably well with previous results observed in homogeneous shear incompressible flows.

^{[13]}In this work, the Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed.

^{[14]}

## isotropic turbulent flow

What makes this model different is that it can describe strongly anisotropic turbulent flows; moreover, it is easy to implement numerically while not being computationally expensive.^{[1]}We investigate the dynamics of turbulent dispersion by means of direct numerical simulations of a passive tracer released in a homogeneous isotropic turbulent flow.

^{[2]}To enable an analysis uncomplicated by the presence of many coupled interactions, we confine our attention to the classic test case of monodisperse particles in homogeneous, isotropic turbulent flows, and subject to a uniform gravitational field.

^{[3]}Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered.

^{[4]}1 library, we study the flow of particles inside a highly anisotropic turbulent flow field of a hydrocyclone.

^{[5]}In this work, a numerical study of the dynamical behavior of unsteady and anisotropic turbulent flow downstream a 90° bended pipe was presented.

^{[6]}We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a stochastic vector field with a Gaussian distribution, and then a scalar advected by a homogeneous and isotropic turbulent flow described by the Navier-Stokes equation, under the assumption that the scalar is passive, i.

^{[7]}The 3D PTV and particle identification algorithms show good consistencies under two types of flow conditions: a homogeneous isotropic turbulent flow and a vortex ring flow.

^{[8]}In this paper we study finite particle Reynolds number effects up to $Re_p=50$ on the dynamics of small spherical bubbles and solid particles in an isotropic turbulent flow.

^{[9]}In addition, the work also consists of implementing an appropriate turbulence model, to ensure a better analysis of free, homogeneous isotropic turbulent flows.

^{[10]}We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations.

^{[11]}The Reynolds stress data showed an anisotropic turbulent flow immediately downstream of the roller toe, and tended towards isotropy away from the roller toe.

^{[12]}In this strongly anisotropic situation, despite the additional roughness induced by the canopy, it is shown that fluctuations of Lagrangian velocity increments over small time scales display very similar behaviour as those observed in homogeneous and isotropic turbulent flows.

^{[13]}Vortices motion in the anisotropic turbulent flow of cyclones makes a vital impact on flow stability and collection performance.

^{[14]}Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered.

^{[15]}The method is demonstrated for a canonical Burgers vortex, a Bodewadt vortex, homogeneous isotropic turbulent flow, the wake of a propeller, a heaving plate, a turning containership and the airwake of a surface combatant.

^{[16]}The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated.

^{[17]}Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively.

^{[18]}Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum.

^{[19]}Validation of the GRM method is carried out by generating and simulating a decaying homogeneous isotropic turbulent flow.

^{[20]}This review devoted to the theoretical analysis, calculation, and modeling of the processes of merging and breakage of droplets and bubbles in an isotropic turbulent flow.

^{[21]}A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero.

^{[22]}EnglishBy using an active grid and a passive grid, a homogenous and isotropic turbulent flow was characterized by studying its longitudinal structure functions and transverse 〉 and where u is the longitudinal velocity fluctuation, and v is the fluctuation of the transverse velocity, as a function of the Reynolds number for orders, n, between 2 and 8.

^{[23]}We propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and fluid inertia forces in a homogeneous and isotropic turbulent flow.

^{[24]}A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero.

^{[25]}An artificial neural network (ANN) is used to establish the relation between the resolved-scale flow field and the subgrid-scale (SGS) stress tensor, to develop a new SGS model for large-eddy simulation (LES) of isotropic turbulent flows.

^{[26]}In this work, the Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed.

^{[27]}To validate this approach, it was applied to an experimental homogeneous and isotropic turbulent flow (HIT), perturbed by a synthetic Lamb–Oseen vortex that mimics the feature of organized motion.

^{[28]}

## isotropic turbulent field

The physical mechanisms underlying the dynamics of the flame kernel in stationary isotropic and anisotropic turbulent field are studied using large eddy simulations (LES) combined with a pdf approach method for the combustion model closure.^{[1]}Homogeneous and isotropic turbulent fields obtained from two DNS databases (with $\mbox{Re}_\lambda$ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories.

^{[2]}The difference in pitch angle of the regular and the ordered fields indicates that the ordered field contains a significant fraction of an anisotropic turbulent field that has a different pattern than the regular (ASS + BSS) field.

^{[3]}

## isotropic turbulent velocity

A distribution of Hill’s vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor.^{[1]}A method for the numerical generation of anisotropic turbulent velocity fields is presented.

^{[2]}On the base of Randomized Spectral Method (RSM), a new stochastic algorithm for the generation of homogeneous anisotropic turbulent velocity fields has been developed.

^{[3]}

## isotropic turbulent cascade

We also show that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with kinetic Alfven wave-like fluctuations from the anisotropic turbulent cascade.^{[1]}We also find that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with fluctuations from the anisotropic turbulent cascade.

^{[2]}

## isotropic turbulent case

Many flow configurations in nature and in the laboratories deviate from the ideal homogeneous and isotropic turbulent cases (HIT) characterised by the presence of direct energy cascade only and strong small-scales universality.^{[1]}The alignment between strain and mixture fraction gradient differs slightly from the homogeneous isotropic turbulent case but agree remarkably well with previous results observed in homogeneous shear incompressible flows.

^{[2]}

## isotropic turbulent structure

In the wall-normal direction, particle distributions (mean/preferential concentration) exhibit two distinct behaviours in the inner flow and outer flow, corresponding to two highly anisotropic turbulent structures, LSMs and VLSMs.^{[1]}The shear-layer involves anisotropic turbulent structures; thus, hybrid RANS/LES models, such as IDDES, are preferred over URANS.

^{[2]}

## isotropic turbulent eddy

Generally, the theory correctly predicts the measured log-amplitude variances, which are affected primarily by small-scale, isotropic turbulent eddies.^{[1]}By improving the aerodynamic shape of the aircraft, it can produce a large number of anisotropic turbulent eddies which can effectively improve the passive jamming capability when the foil is cast.

^{[2]}