Deviations from the classical Kolmogorov theory of the inertial range of homogeneous turbulence

1989 ◽  
Vol 1 (2) ◽  
pp. 289-293 ◽  
Author(s):  
Victor Yakhot ◽  
Zhen‐Su She ◽  
Steven A. Orszag
Keyword(s):  
Inertial Range ◽  
Homogeneous Turbulence ◽  
Kolmogorov Theory

Structure and dynamics of homogeneous turbulence: models and simulations

1991 ◽  
Vol 434 (1890) ◽  
pp. 101-124 ◽  
Keyword(s):  
Turbulence Models ◽  
Background Field ◽  
Quantitative Model ◽  
Homogeneous Turbulence ◽  
Strongly Correlated ◽  
Structure And Dynamics ◽  
Localized Structures ◽  
Kolmogorov Theory ◽  
Statistics Of Turbulence ◽  
Random Background

This paper presents a review of recent results on homogeneous turbulence. We discuss results obtained by direct numerical simulation as well as phenomenological models for the interpretation and understanding of these flows. In particular, we show that homogeneous turbulence can be well described in terms of a weakly correlated, random background field that is generally consistent with the classical Kolmogorov theory of turbulence, and strongly correlated, highly localized structures, that are largely responsible for intermittency effects and deviations from Kolmogorov scaling. These results give a unified dynamical picture of turbulence that describes both the energetics and intermittency of homogeneous turbulence, and allows us to develop a quantitative model for the description of the statistics of turbulence at small scales.

LES computations and comparison with Kolmogorov theory for two-point pressure–velocity correlations and structure functions for globally anisotropic turbulence

2000 ◽  
Vol 403 ◽  
pp. 23-36 ◽  
Author(s):  
K. ALVELIUS ◽  
A. V. JOHANSSON
Keyword(s):  
Structure Functions ◽  
Homogeneous Turbulence ◽  
Kolmogorov Equation ◽  
Inertial Subrange ◽  
Order Structure ◽  
Velocity Correlation ◽  
Point Pressure ◽  
Decaying Turbulence ◽  
High Reynolds ◽  
Kolmogorov Theory

A new extension of the Kolmogorov theory, for the two-point pressure–velocity correlation, is studied by LES of homogeneous turbulence with a large inertial subrange in order to capture the high Reynolds number nonlinear dynamics of the flow. Simulations of both decaying and forced anisotropic homogeneous turbulence were performed. The forcing allows the study of higher Reynolds numbers for the same number of modes compared with simulations of decaying turbulence. The forced simulations give statistically stationary turbulence, with a substantial inertial subrange, well suited to test the Kolmogorov theory for turbulence that is locally isotropic but has significant anisotropy of the total energy distribution. This has been investigated in the recent theoretical studies of Lindborg (1996) and Hill (1997) where the role of the pressure terms was given particular attention. On the surface the two somewhat different approaches taken in these two studies may seem to lead to contradictory conclusions, but are here reconciled and (numerically) shown to yield an interesting extension of the traditional Kolmogorov theory. The results from the simulations indeed show that the two-point pressure–velocity correlation closely adheres to the predicted linear relation in the inertial subrange where also the pressure-related term in the general Kolmogorov equation is shown to vanish. Also, second- and third-order structure functions are shown to exhibit the expected dependences on separation.

Applicability of Kolmogorov's and Monin's equations of turbulence

1997 ◽  
Vol 353 ◽  
pp. 67-81 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Structure Function ◽  
Structure Functions ◽  
Inertial Range ◽  
Homogeneous Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Local Isotropy ◽  
The Third ◽  
Moderate Reynolds Number ◽  
Wide Range

The equation relating second- and third-order velocity structure functions was presented by Kolmogorov; Monin attempted to derive that equation on the basis of local isotropy. Recently, concerns have been raised to the effect that Kolmogorov's equation and an ancillary incompressibility condition governing the third-order structure function were proven only on the restrictive basis of isotropy and that the statistic involving pressure that appears in the derivation of Kolmogorov's equation might not vanish on the basis of local isotropy. These concerns are resolved. In so doing, results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. These results are applicable to future studies of the approach toward local isotropy. Accuracy of Kolmogorov's equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov's 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov's 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov's and Monin's equations leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

Vorticity and passive-scalar dynamics in two-dimensional turbulence

1987 ◽  
Vol 183 ◽  
pp. 379-397 ◽  
Author(s):  
Armando Babiano ◽  
Claude Basdevant ◽  
Bernard Legras ◽  
Robert Sadourny
Keyword(s):  
Similarity Theory ◽  
Physical Space ◽  
Passive Scalar ◽  
Inertial Range ◽  
Flow Dynamics ◽  
Two Dimensional ◽  
Closure Model ◽  
Coherent Vortices ◽  
Vorticity Transport ◽  
Kolmogorov Theory

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.

Implicit Large Eddy Simulation of Two-Dimensional Homogeneous Turbulence Using Weighted Compact Nonlinear Scheme

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Keiichi Ishiko ◽  
Naofumi Ohnishi ◽  
Kazuyuki Ueno ◽  
Keisuke Sawada
Keyword(s):  
Energy Spectrum ◽  
Inertial Range ◽  
Homogeneous Turbulence ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Eddy Simulation ◽  
Numerical Viscosity ◽  
Large Eddy ◽  
Implicit Large Eddy Simulation

For the aim of computing compressible turbulent flowfield involving shock waves, an implicit large eddy simulation (LES) code has been developed based on the idea of monotonically integrated LES. We employ the weighted compact nonlinear scheme (WCNS) not only for capturing possible shock waves but also for attaining highly accurate resolution required for implicit LES. In order to show that WCNS is a proper choice for implicit LES, a two-dimensional homogeneous turbulence is first obtained by solving the Navier–Stokes equations for incompressible flow. We compare the inertial range in the computed energy spectrum with that obtained by the direct numerical simulation (DNS) and also those given by the different LES approaches. We then obtain the same homogeneous turbulence by solving the equations for compressible flow. It is shown that the present implicit LES can reproduce the inertial range in the energy spectrum given by DNS fairly well. A truncation of energy spectrum occurs naturally at high wavenumber limit indicating that dissipative effect is included properly in the present approach. A linear stability analysis for WCNS indicates that the third order interpolation determined in the upwind stencil introduces a large amount of numerical viscosity to stabilize the scheme, but the same interpolation makes the scheme weakly unstable for waves satisfying kΔx≈1. This weak instability results in a slight increase in the energy spectrum at high wavenumber limit. In the computed result of homogeneous turbulence, a fair correlation is shown to exist between the locations where the magnitude of ∇×ω becomes large and where the weighted combination of the third order interpolations in WCNS deviates from the optimum ratio to increase the amount of numerical viscosity. Therefore, the numerical viscosity involved in WCNS becomes large only at the locations where the subgrid-scale viscosity can arise in ordinary LES. This suggests the reason why the present implicit LES code using WCNS can resolve turbulent flowfield reasonably well.

Turbulence properties in coupled and decoupled stratocumulus-topped boundary layers

2021 ◽  
Author(s):  
Jakub Nowak ◽  
Holger Siebert ◽  
Kai Szodry ◽  
Szymon Malinowski
Keyword(s):  
Boundary Layer ◽  
Latent Heat ◽  
Liquid Water Content ◽  
Inertial Range ◽  
Vertical Transport ◽  
Specific Humidity ◽  
Equal Rate ◽  
Stratocumulus Clouds ◽  
Eastern North Atlantic ◽  
Kolmogorov Theory

<p>In marine atmospheric boundary layer (MBL), turbulence plays an important role in vertical transport of mass, heat and moisture, which is crucial for the emergence and evolution of stratocumulus clouds. We use high resolution in situ measurements of flow velocity, temperature, humidity and liquid water content performed from the helicopter-borne platform ACTOS in the region of Eastern North Atlantic in the course of  ACORES campaign to compare turbulence properties in coupled and decoupled stratocumulus-topped boundary layer. Derived parameters include turbulence kinetic energy, its production and dissipation rates, anisotropy of the inertial range, turbulent fluxes of sensible and latent heat as well as characteristic lengthscales.</p><p>Inside the observed coupled MBL, turbulence is intensively produced by buoyancy at the cloud top and at the surface, and dissipated with equal rate across the entire layer depth. Turbulence is close to isotropic and inertial range exhibits scaling relatively close to that predicted by Kolmogorov theory. Inside the decoupled MBL properties of turbulence in the bottom sub-layer (BSL) vary from those in the cloud and sub-cloud layers, which together form upper sub-layer (USL). Transition in between the BSL and the USL is most pronounced in the gradient of specific humidity. The USL is characterized by weak buoyancy production in the cloud, strong anisotropy of turbulence and the scaling deviating from that predicted by Kolmogorov theory. In BSL, fluxes of buoyancy and latent heat decrease with height from the maximum at the surface down to about zero at the transition.</p><p>In general, results are consistent with the conceptual explanation of decoupling mechanism involving two separated zones of circulation and mixing: surface driven and cloud top driven. Our observations suggest that contrasting turbulence parameters need to be considered together with convection organization in order to properly quantify the vertical transport between ocean surface and stratocumulus cloud.</p>

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