Correlation decay of Lagrangian velocity differences in locally isotropic turbulence

1982 ◽  
Vol 49 (3) ◽  
pp. 253-261 ◽  
Author(s):  
S. Grossmann ◽  
S. Thomae
Keyword(s):  
Isotropic Turbulence ◽  
Correlation Decay ◽  
Lagrangian Velocity

The Dependence of the Time Scale of Relative Lagrangian Motion on the Initial Separation

1998 ◽  
Vol 65 (1) ◽  
pp. 204-208
Author(s):  
J. C. H. Fung
Keyword(s):  
Isotropic Turbulence ◽  
Homogeneous Isotropic Turbulence ◽  
Kinematic Simulation ◽  
Lagrangian Statistics ◽  
Initial Separation ◽  
Velocity Autocorrelation ◽  
Lagrangian Velocity ◽  
Short Time ◽  
Lagrangian Motion ◽  
Statistics Of Turbulence

Kinematic simulation of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed pseudo-Lagrangian velocity autocorrelation functions Rˆ11L(l,t) compare well with theory for a small initial separation l and short time t. We also demonstrate the feasibility of using kinematic simulation as a means of constructing Lagrangian statistics.

Lagrangian velocity correlations in homogeneous isotropic turbulence

1993 ◽  
Vol 5 (11) ◽  
pp. 2846-2864 ◽  
Author(s):  
Toshiyuki Gotoh ◽  
Robert S. Rogallo ◽  
Jackson R. Herring ◽  
Robert H. Kraichnan
Keyword(s):  
Isotropic Turbulence ◽  
Homogeneous Isotropic Turbulence ◽  
Lagrangian Velocity

A measurement of Lagrangian velocity autocorrelation in approximately isotropic turbulence

1974 ◽  
Vol 62 (2) ◽  
pp. 255-271 ◽  
Author(s):  
D. J. Shlien ◽  
S. Corrsin
Keyword(s):  
Isotropic Turbulence ◽  
Coefficient Function ◽  
Mean Flow ◽  
Velocity Autocorrelation ◽  
Velocity Statistics ◽  
Dispersion Data ◽  
Lagrangian Velocity ◽  
Heated Wire ◽  
Heat Dispersion ◽  
The Mean

By measuring the heat dispersion behind a heated wire stretched across a wind tunnel (Taylor 1921, 1935), the Lagrangian velocity autocorrelation was determined in an approximately isotropic, grid-generated turbulent flow. The techniques were similar to previous ones, but the scatter is less. Assuming self-preservation of the Lagrangian velocity statistics in a form consistent with recent measurements of decay in this flow (Comte-Bellot & Corrsin 1966, 1971), a stationary and an approximately self-preserving form for the dispersion were derived and approximately verified over the range of the experiment.Possibly the most important aspect of this experiment is that data were available in the same flow on the simplest Eulerian velocity autocorrelation in time, the correlation at a fixed spatial point translating with the mean flow (Comte-Bellot & Corrsin 1971). Thus, the Lagrangian velocity autocorrelation coefficient function calculated from the dispersion data could be compared with this corresponding Eulerian function. It was found that the Lagrangian Taylor micro-scale is very much larger than the analogous Eulerian microscale (76 ms compared with 6.2ms), contrary to an estimate of Corrsin (1963). The Lagrangian integral time scale is roughly equal to the Eulerian one, being larger by about 25 %.

Lagrangian statistics from direct numerical simulations of isotropic turbulence

1989 ◽  
Vol 207 ◽  
pp. 531-586 ◽  
Author(s):  
P. K. Yeung ◽  
S. B. Pope
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Small Time ◽  
Direct Numerical Simulations ◽  
Time Lags ◽  
Lagrangian Statistics ◽  
Lagrangian Velocity ◽  
Velocity Increments ◽  
Non Gaussian

A comprehensive study is reported of the Lagrangian statistics of velocity, acceleration, dissipation and related quantities, in isotropic turbulence. High-resolution direct numerical simulations are performed on 643 and 1283 grids, resulting in Taylor-scale Reynolds numbers Rλ in the range 38-93. The low-wavenumber modes of the velocity field are forced so that the turbulence is statistically stationary. Using an accurate numerical scheme, of order 4000 fluid particles are tracked through the computed flow field, and hence time series of Lagrangian velocity and velocity gradients are obtained.The results reported include: velocity and acceleration autocorrelations and spectra; probability density functions (p.d.f.'s) and moments of Lagrangian velocity increments; and p.d.f.'s, correlation functions and spectra of dissipation and other velocity-gradient invariants. It is found that the acceleration variance (normalized by the Kolmogorov scales) increases as R½λ - a much stronger dependence than predicted by the refined Kolmogorov hypotheses. At small time lags, the Lagrangian velocity increments are distinctly non-Gaussian with, for example, flatness factors in excess of 10. The enstrophy (vorticity squared) is found to be more intermittent than dissipation, having a standard-deviation-to-mean ratio of about 1.5 (compared to 1.0 for dissipation). The acceleration vector rotates on a timescale about twice the Kolmogorov scale, while the timescales of acceleration magnitude, dissipation and enstrophy appear to scale with the Lagrangian velocity timescale.

Direct simulation of particle dispersion in a decaying isotropic turbulence

1992 ◽  
Vol 242 ◽  
pp. 655-700 ◽  
Author(s):  
S. Elghobashi ◽  
G. C. Truesdell
Keyword(s):  
Particle Motion ◽  
Isotropic Turbulence ◽  
Particle Dispersion ◽  
Time Development ◽  
Solid Particles ◽  
Mean Square ◽  
Lagrangian Velocity ◽  
The Mean ◽  
Simulation Results ◽  
Surrounding Fluid

Dispersion of solid particles in decaying isotropic turbulence is studied numerically. The three-dimensional, time-dependent velocity field of a homogeneous, non-stationary turbulence was computed using the method of direct numerical simulation (DNS). A numerical grid containing 963 points was sufficient to resolve the turbulent motion at the Kolmogorov lengthscale for a range of microscale Reynolds numbers starting from Rλ = 25 and decaying to Rλ = 16. The dispersion characteristics of three different solid particles (corn, copper and glass) injected in the flow, were obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 223 particles for each particle type, and then performing ensemble averaging. The three different particles are those used by Snyder & Lumley (1971), referred to throughout the paper as SL, in their pioneering wind-tunnel experiment. Good agreement was achieved between our DNS results and the measured time development of the mean-square displacement of the particles.The simulation results also include the time development of the mean-square relative velocity of the particles, the Lagrangian velocity autocorrelation and the turbulent diffusivity of the particles and fluid points. The Lagrangian velocity frequency spectra of the particles and their surrounding fluid, as well as the time development of all the forces acting on one particle are also presented. In order to distinguish between the effects of inertia and gravity on the dispersion statistics we compare the results of simulations made with and without the buoyancy force included in the particle motion equation. A summary of the significant results is provided in §7 of the paper.The main objective of the paper is to enhance the understanding of the physics of particle dispersion in a simple turbulent flow by examining the simulation results described above and answering the questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics.

scholarly journals A conditionally cubic-Gaussian stochastic Lagrangian model for acceleration in isotropic turbulence

2007 ◽  
Vol 582 ◽  
pp. 423-448 ◽  
Author(s):  
A. G. LAMORGESE ◽  
S. B. POPE ◽  
P. K. YEUNG ◽  
B. L. SAWFORD
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Stochastic Modelling ◽  
Lagrangian Model ◽  
Small Scale ◽  
New Model ◽  
Lagrangian Velocity ◽  
Dissipation Model

The modelling of fluid-particle acceleration in homogeneous isotropic turbulence in terms of stochastic models for the Lagrangian velocity, acceleration and a dissipation rate variable is considered. The basis for the Reynolds model (A. M. Reynolds, Phys. Rev. Lett. vol. 91, 2003, 084503) is reviewed and examined by reference to direct numerical simulations (DNS) of isotropic turbulence at Taylor-scale Reynolds number (Rλ) up to about 650. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein–Uhlenbeck process and reveal non-Gaussianity of the acceleration conditioned on fluctuations of the pseudo-dissipation rate. The DNS data are used to construct a new stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of small-scale intermittency on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov hypotheses). Non-Gaussianity of the conditionally standardized acceleration probability density function (PDF) is accounted for in terms of model nonlinearity. The large-time behaviour of the new model is that of a velocity-dissipation model that can be matched with DNS data for conditional second-order Lagrangian velocity structure functions. As a result, the diffusion coefficient for the new model incorporates two-time information and its Reynolds-number dependence as observed in DNS. The resulting model predictions for conditional and unconditional velocity autocorrelations and time scales are shown to be in very good agreement with DNS.

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