Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence

Ruetsch, G. R.; Maxey, Martin

doi:10.1063/1.857938

Cited by 178 publications

(95 citation statements)

References 22 publications

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“…These findings are the result of investigations into the origin of intermittency in turbulence. It was found [25,16,27] that there are localized regions of very intense vorticity (more than 4 times the mean value), tubular in shape, with a length to diameter ratio of about 6 [28]. These results have been generally obtained from numerical simulations with RA > 100 which is a microscale Reynolds number far in excess of R,\ -40 in our simulations.…”

Section: Incompressible Homogeneous Shear Flowsupporting

confidence: 67%

Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence

Erlebacher

Sarkar

1993

Physics of Fluids A: Fluid Dynamics

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I _Recent analysis of direct numerical simulations of compressible homogeneous shear flow turbulence has unraveled some of the energy transfer mechanisms responsible for the decrease of kinetic energy production when the flow becomes more compressible. In this complementary study, we focus our attention on the rate of strain tensor. A Helmholtz decomposition of the velocity field leads us to consider a solenoidal and an irrotational rate of strain tensor. Their eigenvalue distributions, eigenvector orientations, and the relative alignment between the eigenvectors and the vorticity and pressure gradient vectors are examined with the use of probability density functions. The irrotational rate of strain tensor is found to have a prefered structure in regions of strong dilatation. This structure depends on the mean shear, and is quite different from that of the solenoidal rate of strain tensor. Compressibility strongly affects the orientation properties of the pressure gradient vector.

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Section: Incompressible Homogeneous Shear Flowsupporting

confidence: 67%

Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence

Erlebacher

Sarkar

1993

Physics of Fluids A: Fluid Dynamics

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“…Numerous studies (e.g. Ruetsch & Maxey 1991) have painted a consistent topological picture of developed, fine-scale turbulence in which sheets of dissipation (high magnitude strain rate) are wrapped around 'worms' of intense enstrophy. Yet figure 6 clearly shows 'tear drop'-shaped distributions of Q and R in a flow that is highly inhomogeneous/anisotropic with wildly varying flow topologies, mirroring the finding of a −5/3 slope in flows at modest Reynolds numbers that are also far from homogeneous/isotropic (e.g.…”

Section: Resultsmentioning

confidence: 99%

Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow

2017

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Tomographic particle image velocimetry experiments were performed in the near field of the turbulent flow past a square cylinder. A classical Reynolds decomposition was performed on the resulting velocity fields into a time invariant mean flow and a fluctuating velocity field. This fluctuating velocity field was then further decomposed into coherent and residual/stochastic fluctuations. The statistical distributions of the second and third invariants of the velocity-gradient tensor were then computed at various streamwise locations, along the centreline of the flow and within the shear layers. These invariants were calculated from both the Reynolds-decomposed fluctuating velocity fields and the coherent and stochastic fluctuating velocity fields. The range of spatial locations probed incorporates regions of contrasting flow physics, including a mean recirculation region and separated shear layers, both upstream and downstream of the location of peak turbulence intensity along the centreline. These different flow physics are also reflected in the velocity gradients themselves with different topologies, as characterised by the statistical distributions of the constituent enstrophy and strain-rate invariants, for the three different fluctuating velocity fields. Despite these differing flow physics the ubiquitous self-similar 'tear drop'-shaped joint probability density function between the second and third invariants of the velocity-gradient tensor is observed along the centreline and shear layer when calculated from both the Reynolds decomposed and the stochastic velocity fluctuations. These 'tear drop'-shaped joint probability density functions are not, however, observed when calculated from the coherent velocity fluctuations. This 'tear drop' shape is classically associated with the statistical distribution of the velocity-gradient tensor invariants in fully developed turbulent flows in which there is no coherent dynamics present, and hence spectral peaks at low wavenumbers. The results presented in this manuscript, however, show that such 'tear drops' also exist in spatially developing inhomogeneous turbulent flows. This suggests that the 'tear drop' shape may not just be a universal feature of fully developed turbulence but of turbulent flows in general.

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“…For most purposes (e.g. in Ruetsch & Maxey 1991; Pumir 1994; Overholt & Pope 1996;Yeung 1998) k max η ≈ 1.5 is usually considered sufficient for passive scalars of Schmidt numbers of 1.0 or less. However, it should be emphasized that, at given R λ and Sc, resolution requirements depend on the nature of the quantity computed.…”

Section: Numerical Simulation Overviewmentioning

confidence: 99%

Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study

2001

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The physical mechanisms underlying the dynamics of the dissipation of passive scalar fluctuations with a uniform mean gradient in stationary isotropic turbulence are studied using data from direct numerical simulations (DNS), at grid resolutions up to 512 3 . The ensemble-averaged Taylor-scale Reynolds number is up to about 240 and the Schmidt number is from ⅛ to 1. Special attention is given to statistics conditioned upon the energy dissipation rate because of their important role in the Lagrangian spectral relaxation (LSR) model of turbulent mixing. In general, the dominant physical processes are those of nonlinear amplification by strain rate fluctuations, and destruction by molecular diffusivity. Scalar dissipation tends to form elongated structures in space, with only a limited overlap with zones of intense energy dissipation. Scalar gradient fluctuations are preferentially aligned with the direction of most compressive strain rate, especially in regions of high energy dissipation. Both the nature of this alignment and the timescale of the resulting scalar gradient amplification appear to be nearly universal in regard to Reynolds and Schmidt numbers. Most of the terms appearing in the budget equation for conditional scalar dissipation show neutral behaviour at low energy dissipation but increased magnitudes at high energy dissipation. Although homogeneity requires that transport terms have a zero unconditional average, conditional molecular transport is found to be significant, especially at lower Reynolds or Schmidt numbers within the simulation data range. The physical insights obtained from DNS are used for a priori testing and development of the LSR model. In particular, based on the DNS data, improved functional forms are introduced for several model coefficients which were previously taken as constants. Similar improvements including new closure schemes for specific terms are also achieved for the modelling of conditional scalar variance. The physical mechanisms underlying the dynamics of the dissipation of passive scalar fluctuations with a uniform mean gradient in stationary isotropic turbulence are studied using data from direct numerical simulations (DNS), at grid resolutions up to 5123 . The ensemble-averaged Taylor-scale Reynolds number is up to about 240 and the Schmidt number is from 1 8 to 1. Special attention is given to statistics conditioned upon the energy dissipation rate because of their important role in the Lagrangian spectral relaxation (LSR) model of turbulent mixing. In general, the dominant physical processes are those of nonlinear amplification by strain rate fluctuations, and destruction by molecular diffusivity. Scalar dissipation tends to form elongated structures in space, with only a limited overlap with zones of intense energy dissipation. Scalar gradient fluctuations are preferentially aligned with the direction of most compressive strain rate, especially in regions of high energy dissipation. Both the nature of this alignment and the timescale of the resulting sc...

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Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence

Abstract: Large and smallscale stirring of vorticity and passive scalar in a 3D temporal mixing layer

Cited by 178 publications

References 22 publications

Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence

Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence

Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow

Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study

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