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Charles Meneveau - One of the best experts on this subject based on the ideXlab platform.
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predicting viscous range Velocity Gradient dynamics in large eddy simulations of turbulence
Journal of Fluid Mechanics, 2018Co-Authors: Perry L Johnson, Charles MeneveauAbstract:The detailed dynamics of small-scale turbulence are not directly accessible in large-eddy simulations (LES), posing a modelling challenge, because many micro-physical processes such as deformation of aggregates, drops, bubbles and polymers dynamics depend strongly on the Velocity Gradient tensor, which is dominated by the turbulence structure in the viscous range. In this paper, we introduce a method for coupling existing stochastic models for the Lagrangian evolution of the Velocity Gradient tensor with coarse-grained fluid simulations to recover small-scale physics without resorting to direct numerical simulations (DNS). The proposed approach is implemented in LES of turbulent channel flow and detailed comparisons with DNS are carried out. An application to modelling the fate of deformable, small (sub-Kolmogorov) droplets at negligible Stokes number and low volume fraction with one-way coupling is carried out and results are again compared to DNS results. Results illustrate the ability of the proposed model to predict the influence of small-scale turbulence on droplet micro-physics in the context of LES.
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a closure for lagrangian Velocity Gradient evolution in turbulence using recent deformation mapping of initially gaussian fields
Journal of Fluid Mechanics, 2016Co-Authors: Perry L Johnson, Charles MeneveauAbstract:The statistics of the Velocity Gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the Velocity Gradient tensor in particular. Stochastic models for the Lagrangian evolution of Velocity Gradients in isotropic turbulence, with closure models for the pressure Hesssian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The Recent Fluid Deformation (RFD) closure introduced the idea of mapping an isotropic Lagrangian pressure Hessian as upstream initial condition using the fluid deformation tensor. Recent work on a Gaussian fields closure, however, has shown that even Gaussian isotropic Velocity fields contain significant anisotropy for the conditional pressure Hessian tensor due to the inherent Velocity-pressure couplings, and that assuming an isotropic pressure Hessian as upstream condition may not be realistic. In this paper, Gaussian isotropic field statistics are used to generate more physical upstream conditions for the recent fluid deformation mapping. In this new framework, known isotropy relations can be satisfied {\it a priori} and no DNS-tuned coefficients are necessary. A detailed comparison of results from the new model, referred to as the recent deformation of Gaussian fields (RDGF) closure, with existing models and DNS shows the improvements gained, especially in various single-time statistics of the Velocity Gradient tensor at moderate Reynolds numbers. Application to arbitrarily high Reynolds numbers remains an open challenge for this type of model, however.
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a closure for lagrangian Velocity Gradient evolution in turbulence using recent deformation mapping of initially gaussian fields
Journal of Fluid Mechanics, 2016Co-Authors: Perry L Johnson, Charles MeneveauAbstract:The statistics of the Velocity Gradient tensor in turbulent flows is of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the Velocity Gradient tensor in particular. Stochastic models for the Lagrangian evolution of Velocity Gradients in isotropic turbulence, with closure models for the pressure Hessian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The recent fluid deformation (RFD) closure introduced the idea of mapping an isotropic Lagrangian pressure Hessian as the upstream initial condition using the fluid deformation tensor. Recent work on a Gaussian fields closure, however, has shown that even Gaussian isotropic Velocity fields contain significant anisotropy for the conditional pressure Hessian tensor due to the inherent Velocity–pressure couplings, and that assuming an isotropic pressure Hessian as the upstream condition may not be realistic. In this paper, Gaussian isotropic field statistics is used to generate more physical upstream conditions for the recent fluid deformation mapping. In this new framework, known isotropy relations can be satisfied by tuning the free model parameters and the original Gaussian field coefficients can be directly used without direct numerical simulation (DNS)-based re-adjustment. A detailed comparison of results from the new model, referred to as the recent deformation of Gaussian fields (RDGF) closure, with existing models and DNS shows the improvements gained, especially in various single-time statistics of the Velocity Gradient tensor at moderate Reynolds numbers. Application to arbitrarily high Reynolds numbers remains an open challenge for this type of model, however.
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pressure hessian and viscous contributions to Velocity Gradient statistics based on gaussian random fields
Journal of Fluid Mechanics, 2014Co-Authors: Michael Wilczek, Charles MeneveauAbstract:Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the Velocity Gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian Velocity Gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian Velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon.
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lagrangian dynamics and models of the Velocity Gradient tensor in turbulent flows
Annual Review of Fluid Mechanics, 2011Co-Authors: Charles MeneveauAbstract:Many fundamental and intrinsic properties of small-scale motions in turbulence can be described using the Velocity Gradient tensor. This tensor encodes interesting geometric and statistical information such as the alignment of vorticity with respect to the strain-rate eigenvectors, rate of deformation and shapes of fluid material volumes, non-Gaussian statistics, and intermittency. In the inertial range of turbulence, similar properties can be described using the coarse-grained or filtered Velocity Gradient tensor. In this article we review various models that aim at understanding these phenomena using a small number of ordinary differential equations, written either as a low-dimensional dynamical system or as a set of stochastic differential equations. Typically these describe the Lagrangian evolution of the Velocity Gradient tensor elements following fluid particles and require models for the pressure Hessian and viscous effects. Sample results from various models are shown, and open challenges are high...
C P Gutierrez - One of the best experts on this subject based on the ideXlab platform.
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supernova 2010ev a reddened high Velocity Gradient type ia supernova
Astronomy and Astrophysics, 2016Co-Authors: C P Gutierrez, S Gonzalezgaitan, Gaston Folatelli, G Pignata, J P Anderson, Mario HamuyAbstract:Aims. We present and study the spectroscopic and photometric evolution of the type Ia supernova (SN Ia) 2010ev. Methods. We obtain and analyze multiband optical light curves and optical/near-infrared spectroscopy at low and medium resolution spanning -7 days to +300 days from the B-band maximum. Results. A photometric analysis shows that SN 2010ev is a SN Ia of normal brightness with a light-curve shape of Δm15(B) = 1.12 ± 0.02 and a stretch s = 0.94 ± 0.01 suffering significant reddening. From photometric and spectroscopic analysis, we deduce a color excess of E(B - V) = 0.25 ± 0.05 and a reddening law of Rv = 1.54 ± 0.65. Spectroscopically, SN 2010ev belongs to the broad-line SN Ia group, showing stronger than average Si II λ6355 absorption features.We also find that SN 2010ev is a high Velocity Gradient SN with vSi = 164 ± 7 km s-1 d-1. The photometric and spectral comparison with other supernovae shows that SN 2010ev has similar colors and velocities to SN 2002bo and SN 2002dj. The analysis of the nebular spectra indicates that the [Fe II] λ7155 and [Ni II] λ7378 lines are redshifted, as expected for a high Velocity Gradient supernova. All these common intrinsic and extrinsic properties of the high Velocity Gradient (HVG) group are different from the low Velocity Gradient (LVG) normal SN Ia population and suggest significant variety in SN Ia explosions.
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supernova 2010ev a reddened high Velocity Gradient type ia supernova
arXiv: High Energy Astrophysical Phenomena, 2016Co-Authors: C P Gutierrez, S Gonzalezgaitan, Gaston Folatelli, G Pignata, J P Anderson, Mario HamuyAbstract:Aims. We present and study the spectroscopic and photometric evolution of the type Ia supernova (SN Ia) 2010ev. Methods. We obtain and analyze multi-band optical light curves and optical-near-infrared spectroscopy at low and medium resolution spanning from -7 days to +300 days from the B-band maximum. Results. A photometric analysis shows that SN 2010ev is a SN Ia of normal brightness with a light curve shape of $\Delta m_{15}(B)=1.12 \pm 0.02$ and a stretch s = $0.94 \pm 0.01$ suffering significant reddening. From photometric and spectroscopic analysis, we deduce a color excess of $E(B - V) = 0.25 \pm 0.05$ and a reddening law of $R_v = 1.54 \pm 0.65$. Spectroscopically, SN 2010ev belongs to the broad-line SN Ia group, showing stronger than average Si II {\lambda}6355 absorption features. We also find that SN 2010ev is a high-Velocity Gradient SN, with a value of $164 \pm 7$ km s$^{-1}$ d$^{-1}$. The photometric and spectral comparison with other supernovae shows that SN 2010ev has similar colors and velocities to SN 2002bo and SN 2002dj. The analysis of the nebular spectra indicates that the [Fe II] {\lambda}7155 and [Ni II] {\lambda}7378 lines are redshifted, as expected for a high Velocity Gradient supernova. All these common intrinsic and extrinsic properties of the high Velocity Gradient (HVG) group are different from the low Velocity Gradient (LVG) normal SN Ia population and suggest significant variety in SN Ia explosions.
Mario Hamuy - One of the best experts on this subject based on the ideXlab platform.
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supernova 2010ev a reddened high Velocity Gradient type ia supernova
Astronomy and Astrophysics, 2016Co-Authors: C P Gutierrez, S Gonzalezgaitan, Gaston Folatelli, G Pignata, J P Anderson, Mario HamuyAbstract:Aims. We present and study the spectroscopic and photometric evolution of the type Ia supernova (SN Ia) 2010ev. Methods. We obtain and analyze multiband optical light curves and optical/near-infrared spectroscopy at low and medium resolution spanning -7 days to +300 days from the B-band maximum. Results. A photometric analysis shows that SN 2010ev is a SN Ia of normal brightness with a light-curve shape of Δm15(B) = 1.12 ± 0.02 and a stretch s = 0.94 ± 0.01 suffering significant reddening. From photometric and spectroscopic analysis, we deduce a color excess of E(B - V) = 0.25 ± 0.05 and a reddening law of Rv = 1.54 ± 0.65. Spectroscopically, SN 2010ev belongs to the broad-line SN Ia group, showing stronger than average Si II λ6355 absorption features.We also find that SN 2010ev is a high Velocity Gradient SN with vSi = 164 ± 7 km s-1 d-1. The photometric and spectral comparison with other supernovae shows that SN 2010ev has similar colors and velocities to SN 2002bo and SN 2002dj. The analysis of the nebular spectra indicates that the [Fe II] λ7155 and [Ni II] λ7378 lines are redshifted, as expected for a high Velocity Gradient supernova. All these common intrinsic and extrinsic properties of the high Velocity Gradient (HVG) group are different from the low Velocity Gradient (LVG) normal SN Ia population and suggest significant variety in SN Ia explosions.
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supernova 2010ev a reddened high Velocity Gradient type ia supernova
arXiv: High Energy Astrophysical Phenomena, 2016Co-Authors: C P Gutierrez, S Gonzalezgaitan, Gaston Folatelli, G Pignata, J P Anderson, Mario HamuyAbstract:Aims. We present and study the spectroscopic and photometric evolution of the type Ia supernova (SN Ia) 2010ev. Methods. We obtain and analyze multi-band optical light curves and optical-near-infrared spectroscopy at low and medium resolution spanning from -7 days to +300 days from the B-band maximum. Results. A photometric analysis shows that SN 2010ev is a SN Ia of normal brightness with a light curve shape of $\Delta m_{15}(B)=1.12 \pm 0.02$ and a stretch s = $0.94 \pm 0.01$ suffering significant reddening. From photometric and spectroscopic analysis, we deduce a color excess of $E(B - V) = 0.25 \pm 0.05$ and a reddening law of $R_v = 1.54 \pm 0.65$. Spectroscopically, SN 2010ev belongs to the broad-line SN Ia group, showing stronger than average Si II {\lambda}6355 absorption features. We also find that SN 2010ev is a high-Velocity Gradient SN, with a value of $164 \pm 7$ km s$^{-1}$ d$^{-1}$. The photometric and spectral comparison with other supernovae shows that SN 2010ev has similar colors and velocities to SN 2002bo and SN 2002dj. The analysis of the nebular spectra indicates that the [Fe II] {\lambda}7155 and [Ni II] {\lambda}7378 lines are redshifted, as expected for a high Velocity Gradient supernova. All these common intrinsic and extrinsic properties of the high Velocity Gradient (HVG) group are different from the low Velocity Gradient (LVG) normal SN Ia population and suggest significant variety in SN Ia explosions.
Chaoqun Liu - One of the best experts on this subject based on the ideXlab platform.
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Principal coordinates and principal Velocity Gradient tensor decomposition
Journal of Hydrodynamics, 2020Co-Authors: Pushpa Shrestha, Charles Nottage, Chaoqun LiuAbstract:Helmholtz Velocity decomposition and Cauchy-Stokes tensor decomposition have been widely accepted as the foundation of fluid kinematics for a long time. However, there are some problems with these decompositions which cannot be ignored. Firstly, Cauchy-Stokes decomposition itself is not Galilean invariant which means under different coordinates, the stretching (compression) and deformation are quite different. Another problem is that the anti-symmetric part of the Velocity Gradient tensor is not the proper quantity to represent fluid rotation. To show these two drawbacks, two counterexamples are given in this paper. Then “principal coordinate” and “principal decomposition” are introduced to solve the problems of Helmholtz decomposition. An easy way is given to find the Principal decomposition which has the property of Galilean invariance.
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rortex based Velocity Gradient tensor decomposition
Physics of Fluids, 2019Co-Authors: Chaoqun LiuAbstract:Recently, a vector named Rortex was proposed to represent the local fluid rotation [C. Liu et al., “Rortex—A new vortex vector definition and vorticity tensor and vector decompositions,” Phys. Fluids 30, 035103 (2018)]. In this paper, a universal Rortex based Velocity Gradient tensor decomposition is proposed and the relevant local Velocity increment decomposition is provided. Vortex structures in boundary layer transition on a flat plate are analyzed to quantify the local rotational, compression-stretching, and shearing effects. The results demonstrate that vorticity is shearing-dominant, while the rotational part or Rortex in general occupies a small part of vorticity in most areas of this case. In other words, vorticity is a quality representing shearing rather than rotation or vortex in most regions of this case.
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Explicit expressions for Rortex tensor and Velocity Gradient tensor decomposition
Physics of Fluids, 2019Co-Authors: Yisheng Gao, Jian-ming Liu, Chaoqun LiuAbstract:The introduction of Rortex provides a new perspective to investigate the local properties of vortical structures in transitional and turbulent flows, as Rortex offers a new and systematic description of the local fluid rotation, including scalar, vector and tensor forms. Unfortunately, the previous definition of Rortex is not straightforward, which requires the explicit calculation of somewhat cumbersome coordinate rotation. In this letter, a new explicit tensor form of Rortex and the relevant explicit Velocity Gradient tensor decomposition are presented, based on an explicit formula of the Rortex vector. The explicit tensor form represents the real local rotational part of the Velocity Gradient tensor in the original coordinate system. The explicit calculation of coordinate rotations can be totally avoided, which indicates an important improvement of Rortex based Velocity Gradient tensor decomposition.The introduction of Rortex provides a new perspective to investigate the local properties of vortical structures in transitional and turbulent flows, as Rortex offers a new and systematic description of the local fluid rotation, including scalar, vector and tensor forms. Unfortunately, the previous definition of Rortex is not straightforward, which requires the explicit calculation of somewhat cumbersome coordinate rotation. In this letter, a new explicit tensor form of Rortex and the relevant explicit Velocity Gradient tensor decomposition are presented, based on an explicit formula of the Rortex vector. The explicit tensor form represents the real local rotational part of the Velocity Gradient tensor in the original coordinate system. The explicit calculation of coordinate rotations can be totally avoided, which indicates an important improvement of Rortex based Velocity Gradient tensor decomposition.
James R Dawson - One of the best experts on this subject based on the ideXlab platform.
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on Velocity Gradient dynamics and turbulent structure
Journal of Fluid Mechanics, 2015Co-Authors: John Lawson, James R DawsonAbstract:The statistics of the Velocity Gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$ , which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst Velocity Gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by $\unicode[STIX]{x1D63C}$ . Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian Velocity fields. Moreover, it strongly resembles a promising model for Velocity Gradient dynamics recently proposed by Wilczek & Meneveau ( J. Fluid Mech. , vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the $Q$ field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.
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on Velocity Gradient dynamics and turbulent structure
Journal of Fluid Mechanics, 2015Co-Authors: John Lawson, James R DawsonAbstract:The statistics of the Velocity Gradient tensor , which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst Velocity Gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by . Structures are studied through the footprints they leave in conditional averages of the field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the field conditioned upon and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian Velocity fields. Moreover, it strongly resembles a promising model for Velocity Gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.
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invariants of the reduced Velocity Gradient tensor in turbulent flows
Journal of Fluid Mechanics, 2013Co-Authors: Jose Cardesa, Dhiren Mistry, James R DawsonAbstract:In this paper we examine the invariants p and q of the reduced 2 2 Velocity Gradient tensor (VGT) formed from a two-dimensional (2D) slice of an incompressible three-dimensional (3D) flow. Using data from both 2D particle image velocimetry (PIV) measurements and 3D direct numerical simulations of various turbulent flows, we show that the joint probability density functions (p.d.f.s) of p and q exhibit a common characteristic asymmetric shape consistent with hpqi < 0. An explanation for this inequality is proposed. Assuming local homogeneity we derive hpiD 0 and hqiD 0. With the addition of local isotropy the sign ofhpqi is proved to be the same as that of the skewness of @u1=@x1, hence negative. This suggests that the observed asymmetry in the joint p.d.f.s of p‐q stems from the universal predominance of vortex stretching at the smallest scales. Some advantages of this joint p.d.f. compared with that of Q‐R obtained from the full 3 3 VGT are discussed. Analysing the eigenvalues of the reduced strain-rate matrix associated with the reduced VGT, we prove that in some cases the 2D data can unambiguously discriminate between the bi-axial (sheetforming) and axial (tube-forming) strain-rate configurations of the full 3 3 strain-rate tensor.
