scholarly journals NEW EVIDENCE OF DISCRETE SCALE INVARIANCE IN THE ENERGY DISSIPATION OF THREE-DIMENSIONAL TURBULENCE: CORRELATION APPROACH AND DIRECT SPECTRAL DETECTION

2003 ◽  
Vol 14 (04) ◽  
pp. 459-470 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE ◽  
VLADILEN PISARENKO
Keyword(s):  
Energy Dissipation ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Corrections To Scaling ◽  
Developed Turbulence ◽  
Pairwise Correlations ◽  
Spectral Detection ◽  
Simple Variant ◽  
High Reynolds ◽  
New Evidence

We extend the analysis of Ref. 16 showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (≈ 2500) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency f = 1.434 ± 0.007 corresponding to the preferred scaling ratio γ = 2.008 ± 0.006.

Local energy flux and subgrid-scale statistics in three-dimensional turbulence

1998 ◽  
Vol 366 ◽  
pp. 1-31 ◽  
Author(s):  
VADIM BORUE ◽  
STEVEN A. ORSZAG
Keyword(s):  
Energy Transfer ◽  
Energy Dissipation ◽  
Energy Flux ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Inertial Range ◽  
Local Energy ◽  
Subgrid Scale ◽  
Velocity Gradients

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.

AN EXPERIMENTALIST'S VIEW OF DISCRETE AND CONTINUOUS CASCADE MODELS IN FULLY DEVELOPED TURBULENCE

Fractals ◽  
2002 ◽  
Vol 10 (03) ◽  
pp. 321-327 ◽  
Author(s):  
M. GREINER ◽  
B. JOUAULT
Keyword(s):  
Time Series ◽  
Energy Dissipation ◽  
Energy Flux ◽  
Three Dimensional ◽  
One Dimensional ◽  
Developed Turbulence ◽  
Cascade Models ◽  
Cascade Processes ◽  
Multiplicative Cascade ◽  
Spatial Section

In standard experiments, time series of fully developed turbulent fields are recorded in one point, which according to the frozen flow hypothesis can be interpreted as an instantaneous one-dimensional spatial section through a three-dimensional field. This observational reduction in dimensions is absolutely necessary to be taken into account for the explanation of observed multiplier correlations in the energy dissipation field. We demonstrate this for discrete and continuous multiplicative cascade processes, which are empirically known to describe the multifractal energy flux from integral to dissipation scales.

scholarly journals Numerical Investigation on the Hydraulic Properties of the Skimming Flow over Pooled Stepped Spillway

Water ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1478 ◽  
Author(s):  
Shicheng Li ◽  
Jianmin Zhang
Keyword(s):  
Energy Dissipation ◽  
Transverse Direction ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Energy Dissipation Rate ◽  
Spanwise Direction ◽  
Stepped Spillway ◽  
Stepped Spillways ◽  
Aeration Efficiency ◽  
Horizontal Step

Pooled stepped spillway is known for high aeration efficiency and energy dissipation, but the understanding for the effects of pool weir configuration on the flow properties and energy loss is relatively limited, so RNG k − ε εturbulence model with VOF method was employed to simulate the hydraulic characteristics of the stepped spillways with four types of pool weirs. The calculated results suggested the flow in the stepped spillway with staggered configuration of` two-sided pooled and central pooled steps (TP-CP) was highly three dimensional and created more flow instabilities and vortex structures, leading to 1.5 times higher energy dissipation rate than the fully pooled configuration (FP-FP). In FP-FP configuration, the stepped spillway with fully pooled and two-sided pooled steps (FP-TP) and the spillway with fully pooled and central pooled steps (FP-CP), the pressure on the horizontal step surfaces presented U-shaped variation, and TP-CP showed the greatest pressure fluctuation. For FP-TP and FP-CP, the vortex development in the transverse direction presented the opposite phenomenon, and the maximum vortex intensity in TP-CP occurred at Z/W = 0.25, while FP-FP illustrated no significant change in the transverse direction. The overlaying flow velocity distribution in the spanwise direction demonstrated no obvious difference among FP-FP, FP-TP, and FP-CP, while the velocity in TP-CP increased from the axial plane to the sidewalls, but the maximum velocity for all cases were approximately the same.

scholarly journals Inversion formula of multifractal energy dissipation in three-dimensional fully developed turbulence

2006 ◽  
Vol 73 (5) ◽  
Author(s):  
Jian-Liang Xu ◽  
Wei-Xing Zhou ◽  
Hai-Feng Liu ◽  
Xin Gong ◽  
Fu-Cheng Wang ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Inversion Formula ◽  
Three Dimensional ◽  
Fully Developed Turbulence ◽  
Developed Turbulence

The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 2 The influence of stratification

2012 ◽  
Vol 708 ◽  
pp. 45-70 ◽  
Author(s):  
A. Mashayek ◽  
W. R. Peltier
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Instability ◽  
Developed Turbulence ◽  
Wide Range ◽  
Stratified Shear Flow ◽  
High Reynolds ◽  
The Individual ◽  
Secondary Instabilities ◽  
Alternate Routes

AbstractThe linear stability analyses described in Mashayek & Peltier (J. Fluid Mech., vol. 708, 2012, 5–44, hereafter MP1) are extended herein in an investigation of the influence of stratification on the evolution of secondary instabilities to which an evolving Kelvin–Helmholtz (KH) wave is susceptible in an initially unstable parallel stratified shear layer. We show that over a wide range of background stratification levels, the braid shear instability has a higher probability of emerging at early stages of the flow evolution while the secondary convective instability (SCI), which occurs in the eyelids of the individual Kelvin ‘cats eyes’, will remain a relevant and dominant instability at high Reynolds numbers. The evolution of both modes is greatly influenced by the background stratification. Various other three-dimensional secondary instabilities are found to exist over a wide range of stratification levels. In particular, the stagnation point instability (SPI), which was discussed in detail in MP1, may be of great potential importance providing alternate routes for transition of an initially two-dimensional KH wave into fully developed turbulence. The energetics of the secondary instabilities revealed by our simulations are analysed in detail and the preturbulent mixing properties are studied.

scholarly journals Local Turbulent Energy Dissipation Rate in a Vessel Agitated by a Rushton Turbine

2015 ◽  
Vol 36 (2) ◽  
pp. 135-149 ◽  
Author(s):  
Radek Šulc ◽  
Vít Pešava ◽  
Pavel Ditl
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Reynolds Numbers ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Turbulent Fluctuation ◽  
Rushton Turbine ◽  
Turbulent Energy Dissipation Rate ◽  
High Reynolds ◽  
The One

Abstract The scaling of turbulence characteristics such as turbulent fluctuation velocity, turbulent kinetic energy and turbulent energy dissipation rate was investigated in a mechanically agitated vessel 300 mm in inner diameter stirred by a Rushton turbine at high Reynolds numbers in the range 50 000 < Re < 100 000. The hydrodynamics and flow field was measured using 2-D TR PIV. The convective velocity formulas proposed by Antonia et al. (1980) and Van Doorn (1981) were tested. The turbulent energy dissipation rate estimated independently in both radial and axial directions using the one-dimensional approach was not found to be the same in each direction. Using the proposed correction, the values in both directions were found to be close to each other. The relation ε/(N3·D2) ∞ const. was not conclusively confirmed.

scholarly journals Hydraulic Characteristics and Numerical Simulation of the Entrance Section of Ladder-Shaped Spillway

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
X. B. Gu ◽  
Q. H. Wu ◽  
Y. Wang ◽  
H. X. Zhao
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Energy Dissipation Rate ◽  
Numerical Results ◽  
Experimental Results ◽  
Flow State ◽  
Hydraulic Characteristics

The ladder-shaped spillway in a certain reservoir junction is set as the engineering background in the paper. The hydraulic similarly model experiment and three-dimensional numerical simulation of hydraulic characteristics of water flow are performed. The outflow capacity, flow state analysis, velocity distribution, water surface line, pressure, and the energy dissipation rate are analyzed, and experimental results are compared with the numerical results. The conclusions demonstrate that the numerical results of the flow characteristics are very proximate to actual experimental results, the changeable law is the same, and their energy dissipation rate is basically consistent; it shows the feasibility of three-dimensional numerical simulation; the conclusions can provide the basis for the optimization about the flow state of the ladder-shaped spillway in the future.

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