A closure for Lagrangian velocity gradient evolution in turbulence using recent-deformation mapping of initially Gaussian fields

Johnson, Perry L.; Meneveau, Charles

doi:10.1017/jfm.2016.551

Cited by 46 publications

(106 citation statements)

References 75 publications

(108 reference statements)

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“…They all show realistic statistics of, among other properties, the joint probability distribution function (PDF) of the two invariants Q and R, and the peculiar preferential alignment of vorticity with the eigenframe of deformation (we will define precisely these quantities later in the article). Moreover, with different levels of success, they even compared well against more precise estimations of the pressure field, such as conditional averages of the pressure Hessian given an instance of A, and more precisely, of a joint instance of R and Q (Chevillard et al 2008;Meneveau 2011;Chevillard et al 2011;Wilczek & Meneveau 2014;Johnson & Meneveau 2016). Whereas all these closed dynamics have in common to preserve the self stretching term −A 2 , they unfortunately, to our knowledge, give unrealistic statistics when the Reynolds number R e , introduced as a natural free parameter of the closures, becomes too large, preventing the model from reaching the asymptotic limit of infinite Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

“…We are then asking the tensor terms V ij and D ijkl from (1.3) to be, as a necessary condition, also of finite variance. In the framework of additive noise, the diffusion term is deterministic, and the covariance of its elements can be chosen such that it is consistent with a fourth-order isotropic tensor, ensuring furthermore that the trace-free condition imposed by incompressibility is respected (Chevillard et al 2008;Johnson & Meneveau 2016). As for the drift term V ij , let us for example consider the one predicted by the restricted Euler (RE) approximation, that reads in matrix form…”

Section: Introductionmentioning

confidence: 99%

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A multifractal model for the velocity gradient dynamics in turbulent flows

Pereira¹,

Moriconi²,

Chevillard³

2018

J. Fluid Mech.

107

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We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory in isotropic and homogeneous turbulent flows. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in turbulence phenomenology as the intermittency coefficient, gives a realistic picture of velocity gradient statistics at any Reynolds number. To achieve this level of accuracy, we use as a first modelling step a regularized self-stretching term in the framework of the Recent Fluid Deformation (RFD) approximation that was shown to give a realistic picture of small scales statistics of turbulence only up to moderate Reynolds numbers. As a second step, we constrain the dynamics, in the spirit of Girimaji & Pope (1990), in order to impose a peculiar statistical structure to the dissipation seen by the Lagrangian particle. This probabilistic closure uses as a building block a random field that fulfils the statistical description of the intermittency, i.e. multifractal, phenomenon. To do so, we define and generalize to a statistically stationary framework a proposition made by Schmitt (2003). These considerations lead us to propose a non-linear and non-Markovian closed dynamics for the elements of the velocity gradient tensor. We numerically integrate this dynamics and observe that a stationary regime is indeed reached, in which (i) the gradients variance is proportional to the Reynolds number, (ii) gradients are typically correlated over the (small) Kolmogorov time scale and gradients norms over the (large) integral time scale (iii) the joint probability distribution function of the two non vanishing invariants Q and R reproduces the characteristic teardrop shape, (iv) vorticity gets preferentially aligned with the intermediate eigendirection of the deformation tensor and (v) gradients are strongly non-Gaussian and intermittent, a behaviour that we quantify by appropriate high order moments. Additionally, we examine the problem of rotation rate statistics of (axisymmetric) anisotropic particles as observed in Direct Numerical Simulations. Although our realistic picture of velocity gradient fluctuations leads to better results when compared to the former RFD approximation, it is still unable to provide an accurate description for the rotation rate variance of oblate spheroids.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A multifractal model for the velocity gradient dynamics in turbulent flows

Pereira¹,

Moriconi²,

Chevillard³

2018

J. Fluid Mech.

107

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“…The goal of Sciserver is to provide a local environment for data driven science. Sciserver provides a 10 Gigabit Ethernet connection to the Johns Hopkins Turbulence Database [31,37], which is a valuable asset to the present work since it allows to easily download entire snapshots from the database. Sciserver was initially developed to be used in conjunction with the Sloan Digital Sky Survey, in the form of Skyserver, as a nearline analysis tool to the Astronomy database.…”

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confidence: 99%

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

Elsas

Szalay

Meneveau

2018

Journal of Turbulence

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Motivated by interest in the geometry of high intensity events of turbulent flows, we examine spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analyzed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation, and velocity gradient invariants Q and R and their joint spatial distibutions, using data from a direct numerical simulation of isotropic turbulence at Re λ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus a geometric characterization in terms of these sets' correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behavior. Nevertheless the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on the multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow. We show that sets defined by joint conditions on strain and enstrophy, and on Q and R, also display power law scaling of correlation functions, providing further characterization of the complex spatial structure of these intersection sets.arXiv:1708.05409v1 [physics.flu-dyn]

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“…With ever more sophisticated models of the dynamics of the velocity gradient tensor being developed [43,44], and topological analyses being used to elucidate the physics of more complex flows [45,46], we anticipate that a hypothesis testing framework as outlined here, will be of increasing utility.…”

Section: Discussionmentioning

confidence: 99%

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

Keylock

2017

Phys. Rev. Fluids

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A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q > 0) and excess enstrophy production (R < 0). We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q < 0,R < 0) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.

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A closure for Lagrangian velocity gradient evolution in turbulence using recent-deformation mapping of initially Gaussian fields

Cited by 46 publications

References 75 publications

A multifractal model for the velocity gradient dynamics in turbulent flows

A multifractal model for the velocity gradient dynamics in turbulent flows

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

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