Lagrangian Velocity Structure Functions Research Articles

High Order Lagrangian Velocity Statistics in Turbulence

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to R(lambda) = 815 ) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.

A study of the connection between exit-time statistics and relative dispersion using a simple Lagrangian stochastic model

We use a simple stochastic model of relative dispersion to explore the effect of departures from diffusive behaviour on the connection between exit-time statistics and the Richardson constant g for relative dispersion. We present our results as a function of the Lagrangian velocity structure function constant C 0, which is a persistence parameter representing the strength of memory effects. For C 0 → ∞, the model reduces to a diffusive process, for which we have analytical relationships between g and the exit-time statistics, while according to the best estimates from direct numerical simulation C 0∼ 6–7 in three-dimensional turbulence. We calculate the Richardson constant g and the corresponding constants appearing in the inertial sub-range forms for moments of the exit time and of the inverse exit time, for both forward and backward relative dispersion. For C 0 ∼ 6–7, and using model values for the first and third moments of the exit time, we find that the value for g estimated, assuming the diffusive relationships hold, is within about 20% of the ‘true’ value for forward relative dispersion but can be in error by up to a factor of 5 for backward dispersion. The errors are much larger if the corresponding moments of the inverse exit time are used.

Particle trapping in three-dimensional fully developed turbulence

The statistical properties of fluid particles transported by a three-dimensional fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics are investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov time scale, τη, up to one large-eddy turnover time. Our analysis reveals the existence of relatively rare trapping events in vortex filaments which give rise to enhanced intermittency on Lagrangian observables up to 10τη. Lagrangian velocity structure function attain scaling properties in agreement with the multifractal prediction only for time lags larger than those affected by trapping.

Multifractal statistics of Lagrangian velocity and acceleration in turbulence.

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function, and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism, and its merits and limitations are discussed.

Superstatistical mechanics of tracer-particle motions in turbulence.

The Lagrangian stochastic model of Reynolds [Phys. Fluids 15, L1-4 (2003)]] for the accelerations of fluid particles in turbulence is shown to predict precisely the observed Reynolds-number dependency of the distribution of Lagrangian accelerations and the exponents characterizing the observed extended self-similarity scaling of the Lagrangian velocity structure functions. Departures from superstatistics of the log-normal kind are accounted for and their impact upon model predictions is quantified.

Third-order Lagrangian stochastic modeling

The formulation of third-order Lagrangian stochastic models for the hyper-accelerations (time derivative of acceleration) of fluid particles in turbulence is presented. Agreement between model predictions and data from direct numerical simulations [Yeung and Pope, J. Fluid Mech. 207, 531 (1989)] for the Lagrangian velocity structure function and Lagrangian acceleration autocorrelation function is excellent and significantly better than that obtained with a second-order Lagrangian stochastic model. The effects of third-order processes on the turbulent dispersion of fluid particles are found to be significant at Reynolds numbers typical of laboratory-scale experiments and direct numerical simulations and comparable in magnitude to the effects of second-order processes.

The Kolmogorov constant for the Lagrangian velocity spectrum and structure function

The inertial subrange Kolmogorov constant for the Lagrangian velocity structure function C0 is related to the inertial subrange constant for the Lagrangian acceleration spectrum β by C0=πβ. However, Rλ must be greater than about 105 for the inertial subrange of the structure function to be sufficiently wide to accurately determine C0, while values of Rλ greater than 102 are sufficient to determine β. Taking these Rλ limitations into account, the only two known high-quality independent measurements of C0 are 5.5 and 6.4.

A second‐order Lagrangian stochastic model for particle trajectories in inhomogeneous turbulence

AbstractThe second‐order Lagrangian stochastic model of Du et al. for particle trajectories in homogeneous turbulence is extended to inhomogeneous turbulence. the model is shown to be in good agreement with experimental dispersion data for laboratory‐scale convective boundary layers and for a neutrally stable wind‐tunnel boundary layer. the results of numerical simulations suggest that finite Reynolds number effects are not important in determining the mean concentrations of tracer particles dispersing in these flows. Estimates for the value of the Lagrangian velocity structure function constant, obtained by optimizing model agreement with experimental dispersion data, are found to be flow‐dependent.

Reply To 'Comments on the 'Universality of the Lagrangian velocity structure function constant (C0) across different kinds of turbulence’' by A. M. Reynolds

Reply To 'Comments on the 'Universality of the Lagrangian velocity structure function constant (C0) across different kinds of turbulence’' by A. M. Reynolds

A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer

A new method for deriving the Lagrangian decorrelation time scales for inhomogeneous turbulence is described. The expression for the time scales here derived for the convective boundary layer is compared to those estimated by Hanna during the Phoenix experiment. Then the values of C0, the Lagrangian velocity structure function constant, and of Bi, the Lagrangian velocity spectrum constant, were evaluated from the Eulerian velocity spectra and from the Lagrangian time scales derived, under unstable conditions, from Taylor's statistical diffusion theory. The numerical coefficient of the lateral and vertical Lagrangian spectra in the inertial subrange was found equal to 0.21, in good agreement with previous experimental estimates.

UNIVERSALITY OF THE LAGRANGIAN VELOCITY STRUCTURE FUNCTION CONSTANT (C0) ACROSS DIFFERENT KINDS OF TURBULENCE

In this paper, we evaluate the Lagrangian velocity structure function constant, C0, in the inertial subrange by comparing experimental diffusion data and simulation results obtained with applicable Lagrangian stochastic models. We find in several different flows (grid turbulence, laboratory boundary-layer flow and the atmospheric surface layer under neutral stratification) the value for C0 is 3.0 ± 0.5. We also identify the reasons responsible for earlier studies having not reached the present result.

Estimation of the Kolmogorov constant (C) for the Lagrangian structure function, using a second-order Lagrangian model of grid turbulence

We review Sawford’s [Phys. Fluids A 3, 1577 (1991)] second-order Lagrangian stochastic model for particle trajectories in low Reynolds number turbulence, showing that it satisfies a well-mixed constraint for the (hypothetical) case of stationary, homogeneous, isotropic turbulence in which the joint probability density function for the fixed-point velocity and acceleration is Gaussian. We then extend the model to decaying homogeneous turbulence and, by optimizing model agreement with the measured spread of tracers in grid turbulence, estimate that Kolmogorov’s universal constant (C0) for the Lagrangian velocity structure function has the value of 3.0±0.5.