Kolmogorov Theory of Turbulence

2009 ◽  
pp. 6-6 ◽  
Keyword(s):  
Kolmogorov Theory

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

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.

scholarly journals Comparison of turbulence in HII regions and molecular clouds

1991 ◽  
Vol 147 ◽  
pp. 476-479
Author(s):  
C. R. O'Dell
Keyword(s):  
Molecular Clouds ◽  
Center Of Mass ◽  
Hii Regions ◽  
Emission Lines ◽  
General Increase ◽  
Hii Region ◽  
Velocity Relation ◽  
Common Center ◽  
The One ◽  
Kolmogorov Theory

Both the HII Regions and the Molecular Clouds show broadening of their emission lines beyond that expected from thermal motion and this is ascribed to turbulence. Turbulence in molecular clouds generally agrees with a model where the velocity of motion is determined by the Alfv én velocity.Turbulence in Galactic HII Regions and Giant Extragalactic HII Regions can also be studied by the width of the emission lines. The magnitude of the turbulent velocities in these regions are characteristically about 10 km/s. There is a general increase in turbulent velocity with the size of the HII Region, and this relation is close to but different from the one third power dependence expected from the most naive application of Kolmogorov theory. When a detailed study is conducted of each Galactic HII Region by means of the structure function, one finds that there is not agreement with Kolmogorov theory.The Size-Turbulent versus Velocity relation for Galactic HII Regions differs slightly from the better defined velocity relation for Giant Extragalactic HII Regions. This difference is probably due to the fact that the larger extragalactic objects are probably complexes of multiple individual HII Regions. There is no evidence that broadening of extragalactic HII Regions is due to motion about a common center of mass.

Robust Wiener- Kolmogorov theory

1984 ◽  
Vol 30 (2) ◽  
pp. 316-327 ◽  
Author(s):  
K. Vastola ◽  
H. Poor
Keyword(s):  
Kolmogorov Theory

scholarly journals The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
R. Ye. Brodskii ◽  
Yu. P. Virchenko
Keyword(s):  
Stochastic Model ◽  
Basic Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Fragmentation Process ◽  
Kolmogorov Equation ◽  
Infinite Collection ◽  
Kolmogorov Theory

The stochastic model for the description of the so-called fragmentation process in frameworks of Kolmogorov approach is proposed. This model is represented as the branching process with continuum set(0,∞)of particle types. Each typer∈(0,∞)corresponds to the set of fragments having the sizer. It is proved that the branching condition of this process represents the basic equation of the Kolmogorov theory.

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.

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

Estimation of the scale lengths of turbulence from GPS single difference phase observations 

2021 ◽  
Author(s):  
Gaël Kermarrec ◽  
Steffen Schön
Keyword(s):  
Satellite System ◽  
Index Of Refraction ◽  
Empirical Modeling ◽  
Free Atmosphere ◽  
Phase Measurements ◽  
Power Spectral ◽  
Satellite Geometry ◽  
Global Navigation Satellite ◽  
Kolmogorov Theory ◽  
Single Differences

<p>Signals from the Global Navigation Satellite System (GNSS) travel through the whole atmosphere and encounter fluctuations of the index of refraction. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The power spectral density of microwave phase difference can be derived from physical considerations by combining results from the Kolmogorov theory and electromagnetic wave propagation. Four different dominant noise regimes are expected. Their cutoff frequencies can be estimated with the unbiased Whittle Maximum Likelihood estimator; They provide information about the scale lengths of turbulence which are directly linked with the size of the eddies or swirling motion present in the free atmosphere. Dependencies of these parameters with the satellite geometry or the time of the day pave the way for a better comprehension of how tropospheric turbulence acts as correlating GNSS phase observations. The result is less empirical modeling of GNSS phase correlations to improve the positioning results and avoid an overestimation of their precision. We use GPS single differences from 290 m distant antenna positions recorded during two days in 2013 in a common clock experiment at the Physikalisch Technische Bundesanstalt in Braunschweig Germany to explain our methodology, based on adequate filtering of the residuals to mitigate multipath effects.</p>

scholarly journals von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

2012 ◽  
Vol 697 ◽  
pp. 296-315 ◽  
Author(s):  
Minping Wan ◽  
Sean Oughton ◽  
Sergio Servidio ◽  
William H. Matthaeus
Keyword(s):  
Evolution Equations ◽  
Similarity Solutions ◽  
Magnetic Helicity ◽  
Mhd Turbulence ◽  
Third Order ◽  
Length Scales ◽  
Decay Behaviour ◽  
Self Similar ◽  
Implicit Dependence ◽  
Kolmogorov Theory

AbstractWe argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

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