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## Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

Grebenev, V. N.; Oberlack, M.; Grishkov, A. N.
Fonte: Birkhauser Verlag; Basel Publicador: Birkhauser Verlag; Basel
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.45%
We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.; This work was supported by FAPESP (grant No 11/50984-1), DFG Foundation (grant No OB 96/32-1) and partially by RFBR (grant No 11-01-12075-OFIM-2011).

## Estudo de estrutura turbulenta gerada por tanque de grade oscilante observada por PIV; Study design generated by turbulent tank grid oscillating observed by PIV

Vieira, Amanara Potykytã de Sousa Dias
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
46.51%
Um regime ou fluxo turbulento pode ser definido simplificadamente como uma forma de escoamento no qual o movimento de um fluido ocorre de forma aparentemente aleatória. A natureza caótica desse tipo de regime não possibilita que o problema seja abordado de modo determinístico, consequentemente, não pode ser descrito através de expressões analíticas para descrever seu campo de velocidades. Apesar de ser impossível estudar o movimento de cada partícula, pode-se visualizar o problema de forma macroscópica. Utilizando-se de simplificações e generalizações pode-se fazer uso de estudos numéricos em uma tentativa de encontrar uma face determinística do fenômeno, como por exemplo, verificação da isotropia e homogeneidade. A turbulência com estas características é um regime em que as componentes da velocidade no espaço e as velocidades em diferentes pontos do escoamento apresentam parâmetros estatísticos semelhantes. Tais condições não existem na prática, mas pode-se construir equipamentos que produzem escoamentos que se aproximam desta condição. Este trabalho consistiu na verificação das condições de turbulência isotrópica e homogênea em um tanque de grade oscilante. Foi utilizado o método de trilhagem de partículas por fotografia estereoscópica...

## Radiation statistics in homogeneous isotropic turbulence

da Silva, Carlos; Malico, Isabel; Coelho, Pedro
Tipo: Artigo de Revista Científica Formato: 9662 bytes; application/pdf
ENG
Relevância na Pesquisa
46.46%
An analysis of the interaction between turbulence and radiation in statistically stationary (forced) homogeneous and isotropic turbulence has been carried out. A direct numerical simulation (DNS) code was used to generate instantaneous turbulent scalar fields, and the radiative transfer equation (RTE) was solved to provide statistical data of the radiation intensity and absorption coefficient, as well as correlations related to radiative emission and absorption. In addition, the time-averaged RTE was solved and the mean radiation intensity, mean absorption coefficient, and mean radiative emission were computed and compared with those derived from the statistical data. An analysis of the number of samples required to achieve statistically meaningful results is presented, and the influence of the optical thickness of the medium, mean and variance of the temperature and variance of the mean molar fraction of the absorbing species are studied. The moments of the radiation intensity, Planck-mean and incident-mean absorption coefficients, and emission and absorption correlations relevant to the turbulence – radiation interaction (TRI) are calculated. It was found while turbulence yields an increase of the mean blackbody radiation intensity...

## An exploratory investigation of radiation statistics in homogeneous isotropic turbulence

da Silva, Carlos B.; Malico, Isabel; Coelho, Pedro J.; Pereira, José Carlos F.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.67%
A fundamental study of radiation statistics in homogeneous isotropic turbulence is presented. A pseudo-spectral code is used to simulate isotropic turbulence by means of DNS of the full Navier-Stokes equations. The instantaneous scalar data is used to calculate the radiation intensity along a line of sight using the statistical narrow band model. The mean, variance, skewness and flatness of radiation intensity were obtained for conditions observed downstream of the flame tip of a piloted turbulent jet flame, where the statistics of the flow field are close to the ones found in isotropic turbulence. The joint probability density function between the temperature and the radiation intensity is presented, as well as the spectra for the radiation intensity. The present one way coupling philosophy used to connect isotropic turbulence data with radiation computations shows the correct trends and allows one to study the detailed effects of the turbulent characteristics upon the structure of the radiation intensity field.

## Coherent vorticity extraction in 3D homogeneous isotropic turbulence: influence of the Reynolds number and geometrical statistics

Kadoch,Benjamin; Domingues,Margarete Oliveira; Broemstrup,Ingmar; Larcheveque,Lionel; Schneider,Kai; Farge,Marie
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
56.36%
The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256³ subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (R»= 140,240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256³,512³ and 2048³), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the »2 criterion is applied to the filtered flow fields.

## Theoretical aspects of homogenous isotropic turbulence

Moriconi,L.; Rosa,R.
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
46.46%
We review some recent advances on the problem of fully developed turbulence within the mathematical and physical points of view. From the mathematical perspective, we discuss a framework which has been developed for the rigorous treatment of the conventional statistical theory of turbulence and address some of the rigorous results which have been obtained concerning the energy cascade, the energy spectrum, the energy dissipation rate and other physical quantities of turbulent flows. Regarding the physical approach, we focus our attention on the relevance of field theoretical methods in the analysis of dimensionally reduced models (Burgers and two-dimensional incompressible turbulence), the problem of randomly advected scalars, and intermittent fluctuations in homogeneous and isotropic turbulent flows.

## Remarks on Sedov-type Solution of Isotropic Turbulence

Ran, Zheng
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.55%
The assumption of similarity and self-preservation, which permits an analytical determination of the energy decay in isotropic turbulence, has played an important role in the development of turbulence theory for more than half a century. Sedov (1944), who first found an ingenious way to obtain two equations from one. Nonethless, it appears that this problem has never been reinvestigated in depth subsequent to this earlier work. In the present paper, such an analysis is carried out, yielding a much more complete picture of self-preservation isotropic turbulence. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. The general energy spectra and their behavior in different wave number range are investigated.; Comment: 27papges, 0 figures

## Analytical reconstruction of isotropic turbulence spectra based on the Gaussian transform

Wohlbrandt, Attila; Hu, Nan; Guerin, Sebastien; Ewert, Roland
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.51%
The Random Particle Mesh (RPM) method used to simulate turbulence-induced broadband noise in several aeroacoustic applications is extended to realise isotropic turbulence spectra. With this method turbulent fluctuations are synthesised by filtering white noise with a Gaussian filter kernel that in turn gives a Gaussian spectrum. The Gaussian function is smooth and its derivatives and integrals are again Gaussian functions. The Gaussian filter is efficient and finds wide-spread applications in stochastic signal processing. However in many applications Gaussian spectra do not correspond to real turbulence spectra. Thus in turbo-machines the von K\'arm\'an, Liepmann, and modified von K\'arm\'an spectra are more realistic model spectra. In this note we analytically derive weighting functions to realise arbitrary isotropic solenoidal spectra using a superposition of weighted Gaussian spectra of different length scales. The analytic weighting functions for the von K\'arm\'an, the Liepmann, and the modified von K\'arm\'an spectra are derived subsequently. Finally a method is proposed to discretise the problem using a limited number of Gaussian spectra. The effectivity of this approach is demonstrated by realising a von K\'arm\'an velocity spectrum using the RPM method.; Comment: Preprint...

## Sudden relaminarisation and lifetimes in forced isotropic turbulence

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.6%
We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from a chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.; Comment: 6 pages, 8 figures including supplementary material

## Investigation of the transfer and dissipation of energy in isotropic turbulence

Yoffe, Samuel R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.46%
A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a series of runs for freely-decaying turbulence. We explore the use of power-law decay of the total energy to determine an evolved time and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs. We present results for Reynolds numbers up to R{\lambda} = 335 on a 1024^3 lattice. An exploitation of the pseudospectral technique is used to calculate second and third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The K\'arm\'an-Howarth equation (KHE) is studied and a derivation of a new work term presented. The balance of energy represented by the KHE is then investigated. Based on the KHE...

## A Statistical Theory of Homogeneous Isotropic Turbulence

de Divitiis, Nicola
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.58%
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a representation of the fluid motion which is more general than the classical Navier-Stokes equations, where the fluid state variables are expressed in terms of the referential coordinates. The theory is developed according to the following four items: 1) Study of the route toward the turbulence through the bifurcations analysis of the kinematic equations. 2) Referential description of the motion and calculation of the velocity fluctuation using the Lyapunov analysis of the local deformation. 3) Study of the mechanism of the energy cascade from large to small scales through the Lyapunov analysis of the relative kinematics equations of motion. 4) Determination of the statistics of the velocity difference with the Fourier analysis. Each item contributes to the formulation of the theory. The theory gives the connection between number of bifurcations, scales and Reynolds number at the onset of the turbulence and supplies an explanation for the mechanism of the energy cascade which leads to the closure of the von K\'arm\'an-Howarth equation. The theory also gives the statistics of the velocity difference fluctuation and permits the calculation of its PDF. The presented results show that the proposed theory describes quite well the properties of the isotropic turbulence.; Comment: 34 pages...

## On Isotropic Turbulence in the Dark Fluid Universe

Brevik, Iver; Gorbunova, Olesya; Nojiri, Shin'ichi; Odintsov, Sergei D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.46%
As first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, u^2(t) proportional to t^{-6/5}, is used as input in FRW equations in order to investigate how an initial fraction f of turbulent kinetic energy in the cosmic fluid influences the cosmological development in the late, quintessence/phantom, universe. First order perturbative theory to the first order in f is employed. It turns out that both in the Hubble factor, and in the energy density, the influence from the turbulence fades away at late times. The divergences in these quantities near the Big Rip behave essentially as in a non-turbulent fluid. However, for the scale factor, the turbulence modification turns out to diverge logarithmically. As second part of our work, we consider the full FRW equation in which the turbulent part of the dark energy is accounted for by a separate term. It is demonstrated that turbulence occurrence may change the future universe evolution due to dissipation of dark energy. For instance, phantom-dominated universe becomes asymptotically a de Sitter one in the future, thus avoiding the Big Rip singularity.; Comment: 10 pages, no figures, significant revision. Matches published version

## Symmetry and Hamiltonian structure of the scaling equation in isotropic turbulence

Ran, Zheng; Pan, Shuqin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.55%
The assumption of similarity and self-preservation, which permits an analytical determination of the energy decay in isotropic turbulence, has played an important role in the development of turbulence theory for more than half a century. Sedov (1944), who first found an ingenious way to obtain two equations from one. Nonethless, it appears that this problem has never been reinvestigated in depth subsequent to this earlier work. In the present paper, such an analysis is carried out, yielding a much more complete picture of self-preservation isotropic turbulence. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. The general energy spectra and their behavior in different wave number range are investigated. This letter only focus on the scaling equation.; Comment: 8 pages, 2 figures, 1 table

## Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

Schmidt, W.; Hillebrandt, W.; Niemeyer, J. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.51%
The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wavenumber of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that $C\approx 1.7$. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover...

## Internal stresses and breakup of rigid isostatic aggregates in homogeneous and isotropic turbulence

De Bona, Jeremias; Lanotte, Alessandra S.; Vanni, Marco
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.46%
By characterising the hydrodynamic stresses generated by statistically homogeneous and isotropic turbulence in rigid aggregates, we estimate theoretically the rate of turbulent breakup of colloidal aggregates and the size distribution of the formed fragments. The adopted method combines Direct Numerical Simulation of the turbulent field with a Discrete Element Method based on Stokesian dynamics. In this way, not only the mechanics of the aggregate is modelled in detail, but the internal stresses are evaluated while the aggregate is moving in the turbulent flow. We examine doublets and cluster-cluster isostatic aggregates, where the failure of a single contact leads to the rupture of the aggregate and breakup occurs when the tensile force at a contact exceeds the cohesive strength of the bond. Due to the different role of the internal stresses, the functional relationship between breakup frequency and turbulence dissipation rate is very different in the two cases. In the limit of very small and very large values, the frequency of breakup scales exponentially with the turbulence dissipation rate for doublets, while it follows a power law for cluster-cluster aggregates. For the case of large isostatic aggregates it is confirmed that the proper scaling length for maximum stress and breakup is the radius of gyration. The cumulative fragment distribution function is nearly independent of the mean turbulence dissipation rate and can be approximated by the sum of a small erosive component and a term that is quadratic with respect to fragment size.; Comment: 31 pages...

## Probability Distribution of a Passive Scalar in Isotropic Turbulence

Ran, Zheng; Yuan, Xingjie; Wang, Yaoyao
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.61%
In this letter, we present developments of the Hamiltonian approach to problems of the probability distribution for a passive scalar in isotropic turbulence, and also considers specific applications of the modified Prelle-Singer procedure to turbulence models. The following key questions are discussed and solved: what is the general dynamical structure of the resulting scale equation permitted by passive scalar turbulence models? What are the general requirements of the relations between canonical variables and the canonical variabes representation for turbulence by using canonical variables? It is shown that the existence of the Haniltonian representation in turbulence is a privilege of only turbulence systems for which the variational principle of least action is impossible The master equation of the probability distribution of a passive scalar in isotropic turbulence can also be deduced explicitly.; Comment: 7pages,0figures

## Lyapunov Analysis of Homogeneous Isotropic Turbulence

de Divitiis, Nicola
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.51%
The present work studies the isotropic and homogeneous turbulence for incompressible fluids through a specific Lyapunov analysis, assuming that the turbulence is due to the bifurcations associated to the velocity field. The analysis consists in the study of the mechanism of the energy cascade from large to small scales through the Lyapunov analysis of the relative motion between two particles and in the calculation of the velocity fluctuation through the Lyapunov analysis of the local deformation and the Navier-Stokes equations. The analysis provides an explanation for the mechanism of the energy cascade, leads to the closure of the von K\'arm\'an-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.; Comment: 31 pages, 14 figures, Revision of "Lyapunov Analysis of Homogeneous Isotropic Turbulence", Submitted on Phys. Rev. E

## Scaling of conditional Lagrangian time correlation functions of velocity and pressure gradient magnitudes in isotropic turbulence

Yu, Huidan; Meneveau, Charles
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.58%
We study Lagrangian statistics of the magnitudes of velocity and pressure gradients in isotropic turbulence by quantifying their correlation functions and their characteristic time scales. It has been found that the Lagrangian time-correlations of the velocity and pressure gradient tensor and vector elements scale with the locally-defined Kolmogorov time scale, defined from the box-averaged dissipation-rate and viscosity. In this work, we study the Lagrangian time-correlations of the absolute values of velocity and pressure gradients. We explore the appropriate temporal scales with the aim to achieve collapse of the correlation functions. The data used in this study are sampled from the web-services accessible public turbulence database(http://turbulence.pha.jhu.edu). The database archives a pseudo-spectral direct numerical simulation of forced isotropic turbulence with Taylor-scale Reynolds number 433, and supports spatial differentiation and spatial/temporal interpolation inside the database. The analysis shows that the temporal evolution of the auto-correlations of the absolute values are determined not by the local Kolmogorov time-scale but by the local eddy-turnover time scale. However, considerable scatter remains and appears to be reduced only after a further (intermittency) correction factor of the form of $(r/L)^\chi$ is introduced where $L$ is the turbulence integral scale. The exponent $\chi$ varies for different variables. The collapse of the correlation functions for absolute values is...

## On self-similarity properties of isotropic turbulence in numerical simulations of the compressible Euler equations

Schmidt, W.; Hillebrandt, W.; Niemeyer, J. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.6%
We present numerical calculations of the parameters $C_{\nu}$, $C_{\epsilon}$ and $C_{\kappa}$ associated with the common closures for turbulence production, dissipation and diffusion. In the case of homogeneous and isotropic turbulence, these parameters are expected to be statistically scale-invariant within the inertial subrange. In order to scrutinise this conjecture, we utilised a generalisation of the Germano filtering formalism, which is applicable to compressible flows as well. The filtering of data obtained from three-dimensional direct numerical simulations of forced isotropic turbulence with Mach numbers in the range $\sim 0.1...1$ then yielded values of the closure parameters associated with different length scales. The results indicate that the closure parameters are nearly universal for subsonic or moderately transonic flows, although the resolution of $432^{3}$ grid cells in our simulations is not quite sufficient to clearly establish scale invariance. In addition, it was found that the customary assumption of a kinetic Prandtl number of about unity for the gradient-diffusion closure is flawed due to the misalignment between turbulent flux and the gradient of the turbulence energy. Nevertheless, sound correlation can be achieved if the flux magnitude rather than the flux vector is locally matched. This conclusion is particularly useful for the family of subgrid scale models based on the turbulence energy equation. Furthermore...

## A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence

Carroll, Phares L.; Blanquart, G.
Fonte: American Institute of Physics Publicador: American Institute of Physics
Tipo: Article; PeerReviewed Formato: application/pdf