On some kinematic versus dynamic properties of homogeneous turbulence

Shtilman, L.; Spector, M.D.; Tsinober, A.

doi:10.1017/s0022112093000382

Cited by 42 publications

(49 citation statements)

References 11 publications

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“…2b, characterizing the distribution of alignment between the vortex stretching and the vorticity vectors. The curves for DNS and random data are similar to those presented by Shtilman et al (1993), who noted that the alignment between these vectors is also a dynamic characteristic of turbulence, and its asymmetry is associated with positive enstrophy generation. Once again the peaks are less pronounced in the HATS dataset.…”

Section: B Atmospheric Stability and Resolved Velocity Gradient Strusupporting

confidence: 79%

The Local Structure of Atmospheric Turbulence and Its Effect on the Smagorinsky Model for Large Eddy Simulation

2007

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Phenomena such as large-scale shear, buoyancy, and the proximity to the ground surface significantly affect interactions among scales in atmospheric boundary layer turbulent flows. Hence, these phenomena impact parameters that enter subgrid-scale (SGS) parameterizations used in large eddy simulations (LES) of the atmospheric boundary layer. The effects of these phenomena upon SGS parameters have, to date, been studied mostly as functions of the global state of the flow. For instance, the Smagorinsky coefficient has been measured as a function of the mean shear and stability condition of the atmosphere as determined from the average surface heat and momentum fluxes. However, in LES the global average field values are often difficult to determine a priori and the SGS parameters ideally must be expressed as a function of local flow variables that characterize the instantaneous flow phenomena. With the goal of improving the Smagorinsky closure, in this study several dimensionless parameters characterizing the local structure and important dynamical characteristics of the flow are defined. These local parameters include enstrophy, vortex stretching, self-amplification of strain rate, and normalized temperature gradient and all are defined in such a way that they remain bounded under all circumstances. The dependence of the Smagorinsky coefficient on these local parameters is studied a priori from field data measured in the atmospheric surface layer and, as a reference point, from direct numerical simulation of neutrally buoyant, isotropic turbulence. To capture the local effects in a statistically meaningful fashion, conditional averaging is used. Results show various important and interrelated trends, such as significant increases of the coefficient in regions of large strain-rate self-amplification and vortex stretching. Results also show that the joint dependence on the parameters is rather complicated and cannot be described by products of functions that depend on single parameters. Dependence on locally defined parameters is expected to improve the SGS model by sensitizing it to local flow conditions and by enabling possible generalizations of the dynamic model based on conditional averaging.

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Section: B Atmospheric Stability and Resolved Velocity Gradient Strusupporting

confidence: 79%

The Local Structure of Atmospheric Turbulence and Its Effect on the Smagorinsky Model for Large Eddy Simulation

2007

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“…An important case where the origin of a dynamical effect is unclear is the alignment of the middle eigenvector (associated with the middle eigenvalue) of the rate of strain tensor with the vorticity. This alignment is not seen in Gaussian or random turbulence (Shtilman et al 1992). Ashurst et al (1987) and Vincent & Meneguzzi (1991) have observed such an alignment in Direct Numerical Simulations and believed it to arise from poorly understood nonlinear effects.…”

Section: Structures and Dynamics In Distorted Turbulencementioning

confidence: 95%

Rapid Distortion Theory and the structure of turbulence

Hunt

Kevlahan

1993

New Approaches and Concepts in Turbulence

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This is a review of how, when linear distortions are applied to turbulent velocity fields, certain changes to some or all components of the turbulence can be calculated using linear theory. Important examples of such distortions are mean and random straining motions, body forces, interactions with other flows (eg. waves). This theory is usually known as Rapid Distortion Theory (RDT) because it is valid for all kinds of rapidly changing turbulent flows (RCT), when the distortion is applied for a time (defined in a Lagrangian frame) T D that is short compared to the 'turn-over' or decorrelation time scales T L or τ D (k) of the energy containing eddies or smaller eddies of scale k −1 , respectively. However, for certain kinds of distortion the theory is also applicable to slowly changing turbulence (SCT) where T D is of the order or greater than T L .New insight about the structure of slowly changing turbulence has been derived from RDT by considering different strain rates, initial conditions and time scales. RDT calculations show that in shear flows, whatever the initial form of the energy spectrum E(k) (provided it decreases with wavenumber k faster than k −2 ) or of the anisotropy, for a long enough period of strain, E(k) always tends to the limiting form where it is proportional to k −2 for the small scales. Other statistical properties, such as ratios of Reynolds stresses, are also insensitive to the initial conditions. By contrast RDT shows how turbulent flows without mean strain or with irrotational strain are significantly more sensitive to initial and external conditions. These conclusions are consistent with those drawn from Direct Numerical Simulations (DNS) and experiments at moderate Reynolds numbers.The eddy structure of small scale turbulence can be studied by calculating the distortion of random Fourier components in a velocity field caused by different kinds of large scale straining motions. This method is used here in conjunction with an analysis of how the different types of straining motions in different regions of the small-scale turbulence are affected by the distortion. Interestingly, linear analysis shows that the vorticity vector tends to become aligned with the middle eigenvector of the rate of strain tensor, which is consistent with DNS for turbulent flows having a continuous spectrum.At sufficiently high values of the Reynolds number, even in homogeneous and inhomogeneous distorted turbulence (mean straining flows, body forces and boundaries), the nonlinear processes act over a wide enough spectrum to ensure that at small scales 1 the energy spectrum E(k) has an approximately universal form (as proposed by Kolmogorov). However, at the same time different components of the spectrum have an anisotropic structure. This can be estimated by applying RDT to each wavenumber component of the spectrum and taking the time of distortion to be approximately equal to the turnover time t(k) appropriate to the value of k.

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“…In the case of stretching of vorticity, one always has ω ω ω ≡ 0 which means that vorticity vector is unaffected by the antisymmetric part of the velocity gradient tensor. It was argued in [8] that in the context of 3D flows the angle γ ω = ∠(Dω Dω Dω, ω ω ω) between vorticity and the so called 'vortex stretching' vector has particularly interesting properties. In our case the equivalent would be γ ∇ω = ∠(D D D∇ ∇ ∇ω ω ω, ∇ ∇ ∇ω ω ω).…”

Section: Characterization Of Geometrical Alignmentsmentioning

confidence: 99%

On Geometrical Alignment Properties of Two-Dimensional Forced Turbulence

Protas¹,

Babiano²

1998

Fluid Mechanics and Its Applications

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In the present paper we study some geometrical properties of the small scales in 2D numerical turbulence. We analyze the alignment of the vorticity gradient with respect to the eigenvectors of the rate of strain tensor, a phenomenon related to the dynamics of the enstrophy cascade. Numerical simulations with different resolutions and dissipation models are used to show non-trivial dependence of the alignment on both the magnitude of the vorticity gradient and the Reynolds number. These findings are shown to be dynamical in origin and imply organization of the small scales in the flow.

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On some kinematic versus dynamic properties of homogeneous turbulence

Cited by 42 publications

References 11 publications

The Local Structure of Atmospheric Turbulence and Its Effect on the Smagorinsky Model for Large Eddy Simulation

The Local Structure of Atmospheric Turbulence and Its Effect on the Smagorinsky Model for Large Eddy Simulation

Rapid Distortion Theory and the structure of turbulence

On Geometrical Alignment Properties of Two-Dimensional Forced Turbulence

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