Response of Reynolds stresses and scaling behavior of high-order structure functions to a water-worked gravel-bed surface and its implication on sediment transport

The scaling behaviour of high-order structure functions Gp(r) =〈(u(x+r)−u(x))p〉 is studied in a variety of laboratory turbulent flows. The statistical accuracy of the structure function benefits from novel instrumentation for its real-time measurement. The nature of statistical errors is discussed extensively. It is argued that integration times must increase for decreasing separations r. Based on the statistical properties of probability density functions we derive a simple estimate of the required integration time for moments of a given order. We further give a way for improving this accuracy through careful extrapolation of probability density functions of velocity differences.Structure functions are studied in two different kinematical situations. The (standard) longitudinal structure functions are measured using Taylor's hypothesis. In the transverse case an array of probes is used and no recourse to Taylor's hypothesis is needed. The measured scaling exponents deviate from Kolmogorov's (1941) prediction, more strongly so for the transverse exponents.The experimental results are discussed in the light of the multifractal model that explains intermittency in a geometrical framework. We discuss a prediction of this model for the form of the structure function at scales where viscosity becomes of importance.

Download Full-text

A digital device for measuring high‐order structure functions

Review of Scientific Instruments ◽

10.1063/1.1144828 ◽

1994 ◽

Vol 65 (5) ◽

pp. 1786-1787 ◽

Cited By ~ 6

Author(s):

J. A. Herweijer ◽

F. C. van Nijmweegen ◽

K. Kopinga ◽

J. H. Voskamp ◽

W. van de Water

Keyword(s):

Structure Functions ◽

High Order ◽

Order Structure ◽

High Order Structure ◽

Digital Device

Download Full-text

QUASI-CLOSURE AND SCALING OF TURBULENCE

International Journal of Modern Physics B ◽

10.1142/s0217979201004514 ◽

2001 ◽

Vol 15 (08) ◽

pp. 1085-1116 ◽

Cited By ~ 3

Author(s):

J. QIAN

Keyword(s):

Reynolds Number ◽

Isotropic Turbulence ◽

Structure Functions ◽

High Order ◽

Order Structure ◽

High Order Structure ◽

Homogeneous Isotropic Turbulence ◽

Anomalous Scaling ◽

Closure Scheme ◽

Non Gaussian

A statistically stationary isotropic turbulence is of quasi-closure, i.e. its high-order statistical moments can be derived from its low-order moments. A workable quasi-closure scheme is developed for the structure functions of incompressible homogeneous isotropic turbulence based upon a non-Gaussian statistical model. The second order structure function is obtained by solving the spectral dynamic equation or by using an empirical formula such as the Batchelor fit, and then the high-order structure functions is calculated by the quasi-closure scheme. We study the absolute and relative scaling of the structure functions of isotropic turbulence in connection with Kolmogorovs' 1941 theory (K41) and his 1962 theory (K62). In contrast to K62 and various intermittency models, our results suggest a different picture of scaling of isotropic turbulence: the anomalous scaling of structure functions observed in experiments and numerical simulations is a finite Reynolds number effect, and the K41 normal scaling is valid in the real Kolmogorov inertial range corresponding to an infinite Reynolds number.

Download Full-text