scholarly journals Decay of isotropic turbulence in the initial period

1948 ◽  
Vol 193 (1035) ◽  
pp. 539-558 ◽  
Keyword(s):  
Correlation Function ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Rate Of Change ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Direct Measurements ◽  
Theoretical Predictions ◽  
History Of ◽  
Velocity Correlation Functions

In a previous paper the authors described direct measurements of all the terms in the equation for the rate of change of mean square vorticity in isotropic turbulence. The present paper is concerned with developments arising from the earlier work and with the experimental verification of some recent theoretical investigations. The results of measurements of the turbulent intensity u ' and of λ are presented; these establish that u' -2 and λ 2 are each proportional to the time of decay provided that the time is not too large. Within this initial period of the decay, the double and triple velocity correlation functions are found to maintain their form, i.e. to be self-preserving, for small values of the distance r between the two points at which the correlations are taken. For larger separations the double velocity correlation function changes its form slightly during decay and direct measurements of λ and of the integral scale L show that λ/ L increases during the decay. Theoretical predictions about the shape of the correlation function, for limited ranges of r , at high and at low Reynolds numbers are compared with measurements. Theory has shown that the above decay law cannot persist indefinitely, and the present experiments confirm that the decay law changes in the expected direction when the time is large. A division of the life-history of the turbulence into initial, transition and final periods is suggested; within the initial period, a classification based on the Reynblds number is also possible. Some speculations on the interpretation of the initial period are presented.

scholarly journals The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
V. N. Grebenev ◽  
A. N. Grishkov ◽  
M. Oberlack
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Central Charge ◽  
Riemannian Metrics ◽  
Equivalence Transformation ◽  
Velocity Correlation ◽  
Correlation Tensor

The extended symmetry of the functional of length determined in an affine spaceK3of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variablet) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metricsdl2(t)(Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation spaceK3and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic formdlD22(t)generated bydl2(t)which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric formcas for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame ofdlD22(t).

A comparison of heisenberg's spectrum of turbulence with experiment

1951 ◽  
Vol 47 (1) ◽  
pp. 158-176 ◽  
Author(s):  
Ian Proudman ◽  
G. K. Batchelor
Keyword(s):  
Reynolds Number ◽  
Correlation Functions ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Approximate Form ◽  
Velocity Correlation Functions ◽  
Limiting Case

AbstractIn this paper, the theoretical double and triple velocity correlation functions, f(r), g(r) and h(r), which correspond to Heisenberg's spectrum of isotropic turbulence, are obtained numerically for two Reynolds numbers. One set of these correlations is for the limiting case of infinite Reynolds number. In addition, a method is developed for deriving the approximate form of the double correlations for any Reynolds number, which is not too small, from the corresponding correlations for infinite Reynolds number. These theoretical correlations are then compared with the results of experiment.

scholarly journals Study of Colliding Particle-Pair Velocity Correlation in Homogeneous Isotropic Turbulence

2020 ◽  
Vol 10 (24) ◽  
pp. 9095
Author(s):  
Santiago Lain ◽  
Martin Ernst ◽  
Martin Sommerfeld
Keyword(s):  
Correlation Function ◽  
Turbulent Flow ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Average Kinetic Energy ◽  
Velocity Correlation ◽  
Particle Inertia ◽  
Particle Pair ◽  
Theoretical Approaches

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK~1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles.

Experimental evidence for the theory of local isotropy

1948 ◽  
Vol 44 (4) ◽  
pp. 560-565 ◽  
Author(s):  
A. A. Townsend ◽  
Geoffrey Taylor
Keyword(s):  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Local Isotropy ◽  
High Reynolds Numbers ◽  
Wide Range ◽  
Skewness Factor ◽  
High Reynolds ◽  
Image Position

Some new measurements of isotropic turbulence produced behind a biplane grid have been made at high Reynolds numbers, and these results are compared with the predictions of the theory of local isotropy developed by A. N. Kolmogoroff. The transverse double-velocity correlation has been measured at mesh Reynolds numbers up to 3·2 × 105, and the observed form agrees well with the predicted form. Measurements of the skewness factor of velocity differences over finite intervals have also been made, and the factor is nearly constant and equal to −0·38, if the interval is small compared with the integral scale. The invariance of dimensionless functions of the velocity derivatives has been confirmed for the flattening factor of ∂u/∂x, namely,which is nearly constant over a wide range of conditions. It is concluded that the theory of local isotropy is substantially correct for isotropic turbulence of high Reynolds number.

scholarly journals Decay of vorticity in isotropic turbulence

1947 ◽  
Vol 190 (1023) ◽  
pp. 534-550 ◽  
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Rate Of Change ◽  
Vorticity Equation ◽  
Positive Contribution ◽  
Velocity Correlation ◽  
Negative Contribution ◽  
Velocity Correlation Function ◽  
Rate Of Increase ◽  
Line Elements

The equation describing the rate of change of the mean square vorticity in homogeneous isotropic turbulence is obtained and the terms occurring therein are discussed. A negative contribution to d͞ω 2 / dt arises from the effect of viscosity, while a positive contribution is produced by the tendency for the random diffusive motion to extend the vortex lines. This latter contribution can be related to the skewness of the probability distribution of the rate of extension of line elements of the fluid aligned in any given direction. The results of direct measurements of each of the factors appearing in the vorticity equation are then described. The measurements were made by analyzing electrically the output from a hot-wire anemometer placed downstream from a grid in a uniform stream. Both U 2 / u͞ 2 and ʎ 2 are found to increase approximately linearly with time during decay of the turbulence and their rates of change are consistent with the energy equation. The skewness factor mentioned above is approximately constant during decay, with the same value at all Reynolds numbers. It follows that the rate of increase of ͞ω 2 ¯ due to vortex extension is proportional to ( ͞ω 2 ) 3/2 , and further measurements show that the effect of viscosity has a similar dependence, so that the ratio of the two contributions to d͞ω 2 / dt remains the same throughout the decay. The viscous contribution is always the greater but the contributions tend to equality as the grid Reynolds number increases. The measurements of all terms in the vorticity equation are shown to satisfy the equation with sufficient accuracy. One of the deductions from the measurements is that the double velocity correlation function tends to a cusp at the origin as the Reynolds number increases indefinitely.

scholarly journals Decay of turbulence in the final period

1948 ◽  
Vol 194 (1039) ◽  
pp. 527-543 ◽  
Keyword(s):  
Correlation Coefficient ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Initial Period ◽  
Energy Decay ◽  
Transitional Period ◽  
Asymptotic State ◽  
Time Interval ◽  
Velocity Correlation ◽  
Time Intervals

The final period of decay of a turbulent motion occurs when the effects of inertia forces are negligible. Under these conditions the instantaneous velocity distribution in the turbulence field may be solved as an initial value problem. It is shown that homogeneous turbulence tends to an asymptotic statistical state which is independent of the initial conditions. In this asymptotic state the energy of turbulence is proportional to t -5/2 and the longitudinal double-velocity correlation coefficient for two points distance r apart is e -r2/svt , where t is the time of decay. The asymptotic time-interval correlation coefficient is found to be different from unity for very large time intervals only, showing the aperiodic character of the motion. The whole field of motion comes gradually to rest, smaller eddies decaying more rapidly than larger eddies, and the above stable eddy distribution is established when only the largest eddies of the original turbulence remain. Relevant measurements have been made in the field of isotropic turbulence downstream from a grid of small mesh. The above energy decay and space-interval correlation relations are found to be valid at distances from the grid greater than 400-mesh lengths and at a mesh Reynolds number of 650. The duration of the transitional period, in which the energy decay law is changing from that appropriate to the initial period of decay to the above asymptotic law, increases very rapidly with R M . There is a brief discussion of the criterion for the existence of final period decay, although clarification must wait until the existence and termination of the initial period of decay are better understood.

The measurement of double and triple correlation derivatives in isotropic turbulence

1947 ◽  
Vol 43 (4) ◽  
pp. 560-570 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Isotropic Turbulence ◽  
Hot Wire ◽  
Velocity Correlation ◽  
Integral Scale ◽  
Velocity Fluctuations ◽  
Triple Correlation ◽  
The Third ◽  
Electrical Analysis ◽  
Derivatives Of ◽  
Third Derivative

By electrical analysis of the output from a hot-wire anemometer, it is possible to measure rapidly and accurately all the quantities appearing in the theoretical equations for the decay of isotropic turbulence. The technique for these measurements is described, and possible extensions and limitations of the method are discussed. Measurements have been made of the second and fourth derivatives of the longitudinal double-velocity correlation at the origin, the third derivative of the longitudinal triple-velocity correlation at the origin, the statistical distribution in time of the velocity fluctuations, and the integral scale of turbulence.

A simple turbulence closure hypothesis for the triple-velocity correlation functions in homogeneous isotropic turbulence

1984 ◽  
Vol 140 ◽  
pp. 45-61 ◽  
Author(s):  
J. A. Domaradzki ◽  
G. L. Mellor
Keyword(s):  
Experimental Data ◽  
Correlation Functions ◽  
Eddy Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Laboratory Data ◽  
Reynolds Numbers ◽  
Isotropic Case ◽  
Velocity Correlation ◽  
Viscosity Function

A simple two-point closure scheme for homogeneous axisymmetric turbulence is developed. For the isotropic case it is essentially an eddy-viscosity assumption in real space for the Kármán-Howarth equation. The eddy-viscosity function for large internal Reynolds numbers is derived from Kolmogoroff's 1941 theory. For moderate Reynold's numbers of order 102, approximately the same expression for the eddy-viscosity function is determined from experimental data. The resulting closed equation for the double-correlation function is solved numerically for both large and moderate Reynolds numbers, and the results are compared with experimental data. Self-similar solutions of the basic equation predict turbulent energy decay inversely proportional to time. It is shown that the departure from this ‘initial-period decay law’ observed in laboratory data is due to the behaviour of grid-produced correlation functions for large separation distances.

Triple velocity correlations in isotropic turbulence

1951 ◽  
Vol 47 (1) ◽  
pp. 146-157 ◽  
Author(s):  
R. W. Stewart
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Mean Wind Speed ◽  
The Mean ◽  
Mesh Grid ◽  
Working Section

AbstractThe triple velocity correlation, in turbulence produced by inserting a square-mesh grid near the beginning of the working section of a wind tunnel, has been measured for mesh Reynolds numbers of RM = 5300, 21,200 and 42,400 (RM = UM/ν, where U is the mean wind speed in the working section of the tunnel and M is the centre to centre spacing of the rods making up the grid; ν is the kinematic viscosity of air). At the lowest Reynolds number the correlation has been measured at distances downstream of the grid varying from 20 to 120M. This range covers practically all of the initial period of the decay of turbulence, where the turbulent intensity varies as t−1.

SEJARAH KONFLIK KEBANGKITAN ISLAM DI MINANGKABAU: Sebuah Tinjauan Awal Terhadap Proses Kemunculannya

2018 ◽  
pp. 33-48
Author(s):  
Ihsan Sanusi
Keyword(s):  
Human Life ◽  
Initial Period ◽  
Analysis Model ◽  
Islamic Revival ◽  
Religious Texts ◽  
Interactive Analysis ◽  
The Past ◽  
The Reformation ◽  
History Of ◽  
Correct Understanding

This article in principle wants to examine the history of the emergence of the conflict of Islamic revival in Minangkabau starting from the Paderi Movement to the Youth in Minangkabau. Especially in the initial period, namely the Padri movement, there was a tragedy of violence (radicalism) that accompanied it. This study becomes important, because after all the reformation of Islam began to be realized by reforming human life in the world. Both in terms of thought with the effort to restore the correct understanding of religion as it should, from the side of the practice of religion, namely by reforming deviant practices and adapted to the instructions of the religious texts (al-Qur'an and sunnah), and also from the side of strengthening power religion. In this case the research will be directed to the efforts of renewal by the Padri to the Youth towards the Islamic community in Minangkabau. To discuss this problem used historical research methods. Through this method, it is tested and analyzed critically the records and relics of the past. In analyzing the data in this research basically used approach or interactive analysis model by Miles and Huberman. In this analysis model, the three components of the analysis are data reduction, data presentation, and conclusion drawing or verification, the activity is carried out in an interactive form with the process of collecting data as a process that continues, repeats, and continues to form acycle.

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